Syllogism
TThe word ‘Syllogism’ is also
referred to ‘Logic’. Syllogism is an important section of logical reasoning and
hence, a working knowledge of its rules is required on the part of the
candidate. Hence, it can be expressed as the ‘Science of thought as expressed in
language’. The questions based on syllogism can be solved by using Venn
diagrams and some rules devised with the help of analytical ability. With this
unique characteristic, this test becomes an instrument of teaching the
candidates to follow the rules and work as per the instructions without an
error. Here, only the basic concept and rules, which have a bearing on
reasoning faculty could alone help. There are some terminology which are used
in syllogism.
Proposition
It is also referred to as
‘Premises’. It is a sentence which asserts that either a part of, or the whole
of, one sets of objects-the set identified by the subject term in the sentence
expressing that sentence either is included in, or is excluded from, another
set-the set identified by the predicate term in that sentence.
Types
of Proposition
Categorical
Proposition: There is
relationship between the subject and the predicate without any condition.
Example : I. All beams are logs.
II. No rod is stick.
II. No rod is stick.
Hypothetical
Proposition: There is
relationship between subject and predicate which is asserted conditionally.
Example : I. If it rains he will not
come.
II. If he comes, I will accompany him.
II. If he comes, I will accompany him.
Disjunctive
Proposition In a
disjunctive proposition the assertion is of alteration.
Example : I. Either he is brave or
he is strong.
II. Either he is happy or he cannot take revenge.
II. Either he is happy or he cannot take revenge.
Parts
of Proposition
It
consists of four parts.
1. Quantifier: In quantifier the
words, ‘all’, ‘no’ and ‘some’ are used as they express quantity. ‘All’ and ‘no’
are universal quantifiers because they refer to every object in a certain set.
And quantifier ‘some’ is a particular quantifier because it refers to at least
one existing object in a certain set.
2. Subject: It is the word about
which something is said.
3. Predicate: It is the part of
proposition which denotes which is affirmed or denied about the subject.
4. Copula: It is the part of
proposition which denotes the relation between the subject and predicate.
Four-fold classification of
categorical proposition: On the basis of quality and quantity of proposition we
can classify them in four categories. To draw valid inferences it is necessary
to have a clear
understanding of the A, E, I, O relationship as given in the table.
understanding of the A, E, I, O relationship as given in the table.
1. Universal affirmative or A-type
proposition.
2. Universal negative or E-type
proposition.
3. Particular affirmative or I-type
proposition.
4. Particular negative or O-type
proposition.
Rules
for Mediate Inference
First introduced by Aristotle, a
syllogism is a deductive argument in which conclusion has to be drawn from two
propositions referred to as premises.
Now consider an example.
Statement: I. Vinay is a boy. II. All boys are honest.
Conclusion I. Vinay is honest.
Now consider an example.
Statement: I. Vinay is a boy. II. All boys are honest.
Conclusion I. Vinay is honest.
First two sentences I and II are
called propositions and the sentence I is called conclusion. This conclusion is
drawn from above given two propositions.
Types
of Questions Asked in the Examination
There are mainly two types of
questions which may be asked under this
1. When premises are in specified
form Here premise is in specified form. Here mainly two propositions are given.
Propositions may be particular to universal; universal to particular;
particular to particular; universal to universal.
2. When premises are in jumbled/mixed form Here at least three or more than three proposition are given. Here pair of two propositions out of them follow as same as in specified form.
2. When premises are in jumbled/mixed form Here at least three or more than three proposition are given. Here pair of two propositions out of them follow as same as in specified form.
Type
1 Premises in Specified Forms
Case 1: The conclusion does not
contain the middle term Middle term is the term common to both the premises and
is denoted by M. Hence, for such case, conclusion does not contain any common
term belong to both premises.
Example 1
Statement: I. All men are girls.
II. Some girls are students.
Conclusions I. All girls are men.
II. Some girls are not students.
II. Some girls are students.
Conclusions I. All girls are men.
II. Some girls are not students.
Solution. Since, both the conclusions I and II contain the
middle term ‘girls’ so neither of them can follow. Venn diagram Representation:
All possible cases can be drawn by using Venn diagram.
Analogy (MCQ)
Direction (Q. No. 1-9): Each of the
questions consists of two capitalised words which have a certain relationship
to each other. Followed by four pairs of words. Choose the pair that is related
to each other in the same way as the capitalised pair.
1. PEST :
IRKSOME
(1) salesclerk : courteous
(2) expert : proficient
(3) enigma : unexpected
(4) leader : non-descript
(5) None of these
(1) salesclerk : courteous
(2) expert : proficient
(3) enigma : unexpected
(4) leader : non-descript
(5) None of these
2.
PROLOGUE : NOVEL
(1) preamble : constitution
(2) sketch : drawing
(3) movement : symphony
(4) index : book
(5) None of these
(1) preamble : constitution
(2) sketch : drawing
(3) movement : symphony
(4) index : book
(5) None of these
3. EXPAND
: VOLUME
(1) ascent : flight
(2) proliferate : number
(3) bend : flexibility
(4) cool : temperature
(5) None of these
(1) ascent : flight
(2) proliferate : number
(3) bend : flexibility
(4) cool : temperature
(5) None of these
4. RUST :
CORROSION
(1) vapour : flammability
(2) dew : condensation
(3) crystal : purification
(4) solution : precipitation
(5) None of these
(1) vapour : flammability
(2) dew : condensation
(3) crystal : purification
(4) solution : precipitation
(5) None of these
5. CLAIM :
LEGITIMATED
(1) hypothesis : confirmed
(2) verdict : appealed
(3) counterargument : doubted
(4) proposition : repeated
(5) None of these
(1) hypothesis : confirmed
(2) verdict : appealed
(3) counterargument : doubted
(4) proposition : repeated
(5) None of these
6. CRIME :
PUNISHMENT
(1) lawyer : judge
(2) court : room
(3) accused : defendant
(4) homicide : penalty
(5) None of these
(1) lawyer : judge
(2) court : room
(3) accused : defendant
(4) homicide : penalty
(5) None of these
7. NUTS :
BOLTS
(1) nitty : gritty
(2) bare : feet
(3) naked : clothed
(4) hard : soft
(5) None of these
(1) nitty : gritty
(2) bare : feet
(3) naked : clothed
(4) hard : soft
(5) None of these
8. BEE :
HONEY
(1) wolf : cub
(2) spider : web
(3) goat : cheese
(4) ant : hill
(5) None of these
(1) wolf : cub
(2) spider : web
(3) goat : cheese
(4) ant : hill
(5) None of these
9.
TRANSISTOR : RADIO
(1) sound : stereo
(2) sand : grains
(3) awl : wrench
(4) cement : driveway
(5) None of these
(1) sound : stereo
(2) sand : grains
(3) awl : wrench
(4) cement : driveway
(5) None of these
Probability
Probability
Probability is used to indicate a
possibility of an event to occur. It is often used synonymously with chance.
- In any experiment if the result of an experiment is unique or certain, then the experiment is said to be deterministic in nature.
- If the result of the experiment is not unique and can be one of the several possible outcomes then the experiment is said to be probabilistic in nature.
Various
Terms Used in Defining Probability
(i) Random Experiment: Whenever an
experiment is conducted any number of times under identical conditions and if
the result is not certain and is any one of the several possible outcomes, the
experiment is called a trial or a random experiment, the outcomes are known as
events.
eg, When a die is thrown is a trial, getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event.
eg, When a die is thrown is a trial, getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event.
(ii) Equally Likely Events: Events
are said to be equally likely when there is no reason to expect any one of them
rather than any one of the others.
eg, When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial, the six events are equally likely.
eg, When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial, the six events are equally likely.
(iii) Exhaustive Events: All the
possible events in any trial are known as exhaustive events. eg, When a die is
thrown, there are six exhaustive events.
(iv) Mutually Exclusive Events: If
the occurrence of any one of the events in a trial prevents the occurrence of
any one of the others, then the events are said to be mutually exclusive
events. eg, When a die is thrown the event of getting faces numbered 1 to 6 are
mutually exclusive.
Classical
Definition of Probability
If in a random experiment, there are
n mutually exclusive and equally likely elementary events in which n elementary
events are favourable to a particular event E, then the probability of the
event E is defined as P (E)
• If the probability of occurrence
of an event E is P(E) and the probability of non-occurrence is P, then,
the sum of the probabilities
of success and failure is 1. Also, 0 ≤ P(E) ≤ 1 and 0 ≤ P ≤ 1.
• If P(E) = 1, the event E is called
a certain event and if P(E) = 0, the event E is called an impossible event.
• If E is an event, then the odds in
favour of E are defined as P(E) : P(E) and the odds against E are defined
as P(E): P. Hence, the odds in
favour of E are
the odds against E are
Addition
Theorem on Probability
Independent
and Dependent Events
- Simple Event : An event which cannot be further split is called a simple event. The set of all simple events in a trial is called a sample space.
- Compound Event : When two or more events occur in relation with each other, they are called compound events.
- Conditional Event: If El and E2 are events of a sample space S and if E2 occurs after the occurrence of El, then the event of occurrence of E2 after the event El is called conditional event of E2 given El. It is denoted by E2/El.
‘Smart’
Facts
- When a die is rolled six events occur. They are {1, 2, 3, 4, 5 and 6}
- When two dice are rolled 36 events occur. They are [(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)]
- When a coin is tossed 2 events occur. They are {H, T}
- When two coins are tossed 4 events occur. They are {HH, HT, TH, T T}
- When three coins are tossed 8 events occur. They are {HHH HHT, HTH, HT T, T HH, THT, T TH, T T T}
- In a pack of 52 cards there are 26 red cards and 26 black cards. The 26 red cards are divided into 13 heart cards and 13 diamond cards. The 26 black cards are divided into 13 club cards and 13 spade card. Each of the colours, hearts, diamonds, clubs and spades is called a suit. In a suit, we have 13 cards (ie, A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2)
Mix Graphs
You can compare several
categories by a graph of the cumulative type. These are usually bar or line
graphs where the height of the bar or line is divided up proportionately among
different quantities.
Q. In 1986, roughly what
percent of the federal prisoners received from the courts were guilty in other
offenses?
(a) 10
(b) 15
(c) 25
(d) 30
(b) 15
(c) 25
(d) 30
The total number of prisoners
in 1986 was about 20,000, and guilty in other offences was about 5,000.
Since the correct answer is
(c).
In DI section of the question
paper, the intention should be to attempt all questions as skipping them would
amount to losing precious scoring opportunities. There are two approaches to
arrive at the solution. One is to work on the data to arrive at the correct
answer. The other one is the Elimination method which requires working
backwards by eliminating the wrong choices. Though the elimation method is more
time consuming, it may still be preferred where direct solution involves
enormous calculation of data.
At times, examiners pose rather
difficult data sets at the beginning of the sections. These are intended to be
‘SPEED BRAKERS’ which take away much of precious time. Therefore, as a rule,
scan the whole section quickly before actually attempting the questions and
start with easier part of the section.
In some exams, data are
presented in more than one table or graph. The objective is to test not only
quantitative skills but also relational and analytical ability. Recently, in
some exams the questions in this section are being framed in caselet
(paragraph) form, beginning with probability and reasoning questions. It is
left to the reader to study the case, call out requisite data and arrange it in
a suitable form for meaningful interpretation. It is best to arrange data with
rough sketch to hasten comprehension.
Important Tips: These will help in saving time, reducing mistakes and finding solution easily.
1.
Get a general picture of the
information by looking at the entire table or graph.
2.
Read the table title,
nomenclatures of columns and rows.
3.
Simplify the questions being
asked. Break down lengthy questions into smaller parts.
4.
Use only the information given
for finding solutions. Select the appropriate data for answering a question.
5.
Eliminate impossible choices.
6.
Avoid lengthy calculations.
7.
Try to interpret through trends
of the data in the graph. Whenever possible, try to answer the questions by
visualizing rather than by computing.
8.
Where calculation is required
prefer approximate values at the first stage. Go for exact calculation where
values are close and require exact answer.
9.
Be careful to use proper units.
10. Make correct use of your knowledge of basic mathematical rules,
principles and formulae.
11. Don’t confuse in decimals and percent ages. For example, 0.5% =
0.005.
12. Use pencil or straight edge of the answer sheet to read the graph
and find approximate values.
13. Focus your answer on the question actually asked and not on what the
question should be in your opinion.
14. Never do anything that is unnecessary.
15.
Last, but not the least, make
sure that the answer is sensible and reasonable.
16.
Verbal
17. 1. If Step IV reads ‘to restrict the
use of air conditioners”, which of the following will definitely be the input?
(1)use to of the air conditioners restrict
(2)restrict the to of air conditioners use
(3)the air conditioners of restrict use to
(4) Can’t be determined
(5) None of these
(1)use to of the air conditioners restrict
(2)restrict the to of air conditioners use
(3)the air conditioners of restrict use to
(4) Can’t be determined
(5) None of these
18. Directions: Read the following
information carefully and answer the questions given below:
19. A famous museum issues entry passes
to all its visitors for security reasons. Visitors are allowed in batches after
every one hour. In a day there are six batches. A code is printed on entry pass
which keeps on changing for every batch. Following is an illustration of
pass-codes issued for each batch.
Batch I: clothes neat and clean liked are all by
Batch II: by clothes neat all are and clean liked
Batch III: liked by clothes clean and neat all are and so on…
Batch I: clothes neat and clean liked are all by
Batch II: by clothes neat all are and clean liked
Batch III: liked by clothes clean and neat all are and so on…
20. 2. If pass-code for the third batch
is ‘night succeed day and hard work-to for’, what will be the pass-code for the
sixth batch?
(1)work hard to for succeed night and day
(2)hard work for and succeed night to day
(3)work hard for to succeed night and day
(4)hard work for to succeed night and day
(5) None of these
(1)work hard to for succeed night and day
(2)hard work for and succeed night to day
(3)work hard for to succeed night and day
(4)hard work for to succeed night and day
(5) None of these
21. 3. If ‘visit in zoo should the time
day’ is the pass-code for the fifth batch, zoo we the should visit day time in’
will be the pass-code for which of following batches?
(1) II
(2) IV
(3) I
(4) III
(5) VI
(1) II
(2) IV
(3) I
(4) III
(5) VI
22. 4. Sanjay visited the museum in the
fourth batch and was issued a pass-code ‘to fast rush avoid not do very run’.
What would have been the pass-code for him had he visited the museum in the
second bitch?
(1)rush do not avoid to run very fast
(2)rush not do-avoid to run very
(3)avoid rush not do to run very fast
(4) Date inadequate
(5) None of these
(1)rush do not avoid to run very fast
(2)rush not do-avoid to run very
(3)avoid rush not do to run very fast
(4) Date inadequate
(5) None of these
23. 5. Subodh went to visit the museum
in the second batch. He was issued a pass-code ‘length the day equal of an
night are’. However, he could not visit the museum in the second batch as he
was a little late. He then preferred to visit in the fifth batch. What will be
the new pass-code issued to him?
(1)and of are night the length equal day
(2)and are of night the length equal day
(3)and of are night the equal day length
(4 )an d of are th e night len gth day equal
(5) None of these
(1)and of are night the length equal day
(2)and are of night the length equal day
(3)and of are night the equal day length
(4 )an d of are th e night len gth day equal
(5) None of these
24. 6. If ass-code for the second batch
is ‘to confidence hard you leads work and success’, what will be the pass-code
for the fourth batch?
(1)leads success to you hard confidence and work
(2)leads success you to hard confidence and work
(3)leads success to you hard confidence work and
(4)leads to success you hard confidence and work
(5) None of these
(1)leads success to you hard confidence and work
(2)leads success you to hard confidence and work
(3)leads success to you hard confidence work and
(4)leads to success you hard confidence and work
(5) None of these
25. 7. If the pass-code issued for the
last (sixth) batch is ‘and pencil by all boys used are pen’, what will be the
passcode for the first batch?
(1)pencil and pen are used by all boys
(2)pen and pencil used are by all boys
(3)pen and pencil are used by all boys
(4)Pencil and pen are used all by boys
(5) None of these
(1)pencil and pen are used by all boys
(2)pen and pencil used are by all boys
(3)pen and pencil are used by all boys
(4)Pencil and pen are used all by boys
(5) None of these
26. 8. If the pass-code for the sixth
batch is ‘not go the way to of out do’, what will be the pass-code for the
third batch?
(1)Of do to out go not way the
(2)of to do out not go way the
(3)of to go out do not way the
(4) Data inadequate
(5) None of these
(1)Of do to out go not way the
(2)of to do out not go way the
(3)of to go out do not way the
(4) Data inadequate
(5) None of these
27. Directions: Study the following
information to answer the given questions:
28. A word rearrangement machine when
given an input line of words, rearranges them following a particular rule in
each step. The following is an illustration of input and the steps of
rearrangement:
Input: Over you pat me crow easy to.
Steps: (I) pat over you crow easy to me
Steps: (II) crow pat over you to me easy
Steps: (III) over crow pal to me easy you
Steps: (IV) to over crow pat easy you me and so on.
As per the rule followed in the above steps, find out the appropriate step for the given input in the following questions:
Input: Over you pat me crow easy to.
Steps: (I) pat over you crow easy to me
Steps: (II) crow pat over you to me easy
Steps: (III) over crow pal to me easy you
Steps: (IV) to over crow pat easy you me and so on.
As per the rule followed in the above steps, find out the appropriate step for the given input in the following questions:
29. 9. If Step II of an input is ‘ge su
but he for game free’, what would be step VI?
(1)a for but fine he game su
(2)for free ge game su he but
(3)free ge for but game su he
(4)he ge su but game free for
(5) None of these
(1)a for but fine he game su
(2)for free ge game su he but
(3)free ge for but game su he
(4)he ge su but game free for
(5) None of these
30. 10. If step IV of an input is ‘blue
navy kit lime se get‘, which of the following would definitely be the input?
(1)navy get lime out kit se blue
(2)lime navy get kit se blue out
(3)lime blue navy kit get out se
(4)kit blue navy se get out lime
(5) None of these
(1)navy get lime out kit se blue
(2)lime navy get kit se blue out
(3)lime blue navy kit get out se
(4)kit blue navy se get out lime
(5) None of these
31. 11. Input: but calm free are so not
eat. Which of the following will be the 3rd step for this input?
(1)so free but calm eat are not
(2)but calm are free not so eat
(3)are but calm free not eat so
(4)but so free eat are not calm
(5) None of these
(1)so free but calm eat are not
(2)but calm are free not so eat
(3)are but calm free not eat so
(4)but so free eat are not calm
(5) None of these
32. 12. If step V of an input is ‘put
down col in as mach sa’ , what would be the 8th step?
(1)down in put much sa as col
(2)in put down cot much sa as
(3)much in put down sa as col
(4)col put down as much sa in
(5) None of these
(1)down in put much sa as col
(2)in put down cot much sa as
(3)much in put down sa as col
(4)col put down as much sa in
(5) None of these
33. 13. Input: rim bye eat klin fe to
low Which of the following steps would be ‘fe low rim to bye klin eat’?
(1) VIth
(2) vth
(3) IVth
(4) IIIrd
(5) None of these
(1) VIth
(2) vth
(3) IVth
(4) IIIrd
(5) None of these
34. Directions: A word arrangement
machine, when given a particular input, rearranges it following a particular
rule. The following is the illustration of the input and the steps of
arrangement:
35. Input: Put pocket hand watch he for them.
Step I: Put for he watch hand pocket them.
Step II: Put he for watch pocket hand them.
Step III: Put hand pocket watch for he them.
Step IV: Put pocket hand watch he for them.
And so on goes the machine. Study the logic and answer the questions that follow:
Step I: Put for he watch hand pocket them.
Step II: Put he for watch pocket hand them.
Step III: Put hand pocket watch for he them.
Step IV: Put pocket hand watch he for them.
And so on goes the machine. Study the logic and answer the questions that follow:
36. 14. If Step III of a given input be
‘fly sky birds my su fur say’, what is the seventh step of the input?
(1)fly sky birds my su fur say
(2)fly birds sky my fur su say
(3)fly fur su my birds sky say
(4)fly su fur my sky birds say
(5) None of these
(1)fly sky birds my su fur say
(2)fly birds sky my fur su say
(3)fly fur su my birds sky say
(4)fly su fur my sky birds say
(5) None of these
37. 15. If Step VII of an input is ‘slow
ran dhurwa pat hak dig vi’, what is step V of that input?
(1)slow dig hak pat dhurwa ran vi
(2)slow hak dig pat ran dhurwa vi
(3)slow hak dig pat ran dhurwa vi
(4)slow ran dhurwa pat hak dig vi
(5) None of these
(1)slow dig hak pat dhurwa ran vi
(2)slow hak dig pat ran dhurwa vi
(3)slow hak dig pat ran dhurwa vi
(4)slow ran dhurwa pat hak dig vi
(5) None of these
38.
Answers
39. 1. (2) 2. (3) 3. (4) 4.
(1) 5. (1) 6. (1) 7. (3) 8. (5) 9. (3) 10. (1) 11. (4) 12. (5) 13. (2) 14. (1)
15. (2)
40.
Non Verbal
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
Answers
53. 1. (2) 2. (3) 3. (3) 4.
(4) 5. (2)
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