Nift study material general ability test

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AnalyticalAbility
LOGICAL ARGUMENTS CHAPTER TEN
Set Theory is a basic tool of logical argument. It is a simple concept that focuses on understanding how things relate
to different categories. It is a common trap to inaccurately assign membership of a group (or set) and consequently
make false statements.
Set Theory is best explained using visual overlapping circles, as below. These are called Venn Diagrams. There are also
short-hand symbols that are used to write relationships is a mathematical way. Venn Diagrams are very useful for
clarifying and understanding questions which have ‘This is an X, it is not a Y’ or ‘X and Y have some things in
common’.
The critical first question is to identify to which sets or category something belongs.
Individual members
If A is a member of B (symbolically: A c B); this means that A has all the attributes of B, that A is a B in all respects.
Subsets
Sets can also be nested, so one set is completely within another set (and is hence a subset).
Supersets are the inverse of subsets. Thus, if A is a subset of B, then B is a superset of A.
Negation
When an individual member or a subset is outside of a set, the relationship can be described by using a ‘not’
statement, which is shown symbolically . Although in normal English, we could say ‘Cats are not Dogs’, in Set Theory,
‘not dogs’ means everything that is not dogs.
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AnalyticalAbility
Intersection and Union
Above the level of the individual item, the concern is how sets overlap. When two sets may have some members that
belong to both sets, we can show this as a Venn diagram with overlapping circles.
Intersection
In this diagram, we can look at it in two ways: the overlapping bit and the non-overlapping bit.
The overlapping bit is called the intersection and has members which have attributes of both sets. This is generally used
when the word ‘and’ appears in the question
Union
When both sets are seen as a single set, this is called the union. This happens when the word ‘or’ is used, and may be
written as A + B, where the plus sign means ‘or’ (not the normal arithmetic ‘plus’).
And...
The remaining pieces are a bit odd, as they are the remaining pieces of each set which is not in the other set. Thus
there is ‘A and Not B’ and ‘B and Not A’.
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AnalyticalAbility
Syllogistic traps
We each make many statements in conversation and written statements, implying logical connections between them.
Sadly, the logic and truth that we assume is not always there.
Consider the following statements and conclusion:
Statement 1: All men are animals
Statement 2: Some animals are aggressive
Conclusion: Some men are aggressive
This seems to be a reasonable conclusion, but then consider the following:
Statement 1: All men are animals
Statement 2: Some animals are female
Conclusion: Some men are female
Now the conclusion appears to be ridiculous and false - yet the reasoning is exactly the same as in the first example. The first
example thus has a false conclusion. The animals who are aggressive are not necessarily men.
What is happening here is that we are using what we know to be true as a substitute for the logic of the statement. In less
certain situations, we use the same unspoken assumptions and beliefs to less acceptable ends.
. The diagram below is a valid drawing that explains the first two statements in the example.
The conclusion falls into the traps of making the assumption that the ‘aggressive animals’ and ‘men’ subsets necessarily
overlap, whereas there is no necessity for this in statements one and two. Although the conclusion could be true it does not
have to be true.
So Beware of making linked assertions that seem reasonable but in fact are logically incorrect.
The choice of either of these is called an
exclusive or (the intersection is an inclusive or), and
is ‘A and not B, or not A and B’, which also
may be written as:
A.~B + ~A.B
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AnalyticalAbility
In each questions below are given two statements
followed by two conclusions numbered I and II. You
have to take the given statements to be true, even if they
seem to be at variance from commonly known facts and
then decide which of the given conclusions logically
follows from the statements dis-regarding commonly
known facts. Give answer:
a. If only conclusion I follows
b. If only conclusion II follows
c. If either I and II follows
d. If neither I or II follows and
e. If both I and II follows
Q.1. STATEMENTS:
1. Some jugs are glasses
2. No jug is a cup.
CONCLUSION
1. All glasses are cups
2. Some glasses are cups
Q.2. STATEMENTS
1. Some books are birds
2. Some birds are fingers
CONCLUSION
1. Some fingers are book
2. Some fingers are birds
Q.3. STATEMENTS
1. All books are bushes
2. all trees are bushes
CONCLUSION
1. Some buses are books
2. some bushes are trees
Q.4. STATEMENTS
1. All writers are teachers
2. all teachers are female
CONCLUSION
1. Some teachers are writers
2. All females are teachers
Q.5. STATEMENTS
1. All nails are ears
2. Some ears are eyes
CONCLUSION
1. All ears are nails
2. Some eyes are nails
Q6. STATEMENTS
1. All pilots are brave’ men.
2. All astronauts are pilot.
CONCLUSIONS
1. All astronauts are brave men.
2. Some pilots are astronauts.
Q7. STATEMENTS
1. Many books are rocks.
2. All rocks are clips.
CONCLUSIONS
1. Some books are clips.
2. No rock is a book.
Q8. STATEMENTS
1. Some kites are horses.
2. All horses are dogs.
CONCLUSIONS
1.. All dogs are horses.
2. Some dogs are horses.
.
1. d. If we look at the statements carefully we find that
in both the statement relationship is given with respect
glasses and cup. Therefore ‘d’ is the correct answer.
2. b. No relationship is given between fingers and books
in either of the statement I or II. However inference
that “Some fingers are birds” can be easily drawn
from the statement. Hence only conclusion II follows.
There for b is the answer.
3. a. Only conclusion I follows because no definite
inference can be made about the conclusion II. Hence
a is the answer
4. a. Conclusion I follows from the statement. However
conclusion II does not follow. Hence a is the answer.
5. d. No definite inference can be made either about
conclusion I or conclusion II from the given
statement. Hence neither conclusion I or conclusion
II follows. Therefore d is the ans.
6. a. Since both the premises are affirmative, the
conclusion must be affirmative. So only conclusion
(a) follows
7. d. Since one premise is negative, the conclusion must
be negative. So neither conclusion follows.
8. Since one premise is particular, the conclusion must
be particular. So, only conclusion ‘b’follows.
EXERCISE- 10
SOLUTIONS TO EXERCISE - 10
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AnalyticalAbility
In each of the following questions, a statement is followed by two assumptions I and II. Consider the statement
and decide which of the given assumption is implicit.
Give answer : .
(a) if only assumption ! is implicit;
(b) if only assumption II is implicit;
(c) If either I or II is implicit.
(d) If neither I nor II is implicit; and
(e) If both I and II are implicit.
1. Statement : Let us change the eligibility criteria to reduce the number of applicants.
Assumptions : I. The present eligibility criteria are very low.
II. Large number of applications are not desirable.
The statement never means that the eligibility criteria is very low. It only suggests to reduce the number or
applicants so that the eligibility criteria is raised. Thus assumption I is not implicit. Assumption II does not show the status
of the applicants. So this assumption is also not implicit. Hence both assumption are not implicit.
Ans. (d)
2. Statement: Over 1-4 lakh quintals of cotton has been procured under Cotton Procedure Scheme,
a press note said.
Assumptions : I. Cotton procurement scheme is successful.
II. No cotton procurement should be done now.
The statement given indicates only the amount of cotton procured. There is no mention of the information
containedinassumptionsIorII.HenceneitherassumptionInorassumptionIIisimplicit.
Ans. (d)
3. Statement: The present examination system needs over hauling thoroughly.
Assumptions : I. The present examination system is obsolete.
II. Overhauling results in improvement.
Both the assumptions are implicit overhauling results in improvement and also only obsolete system needs
overhauling.
Ans. (e)
4. Statement: The taste of food contributes to the intake of nourishment which is essential for a
survival of human beings.
Assumptions : I. Human beings take food for the enjoyment of its taste.
II. Human beings experience the taste of food.
Looking into the statement, assumption I does not seem to be implicit since food is not taken by human beings
for enjoyment but for survival. By taking food one can only experience its taste, so assumption II is implicit only.
Ans. (b)
5. Statement: Every year doctors, scientists and engineers migrate from India to greener pastures. .
Assumptions : I. Brain drain has affected India adversely.
II. Better scales and better standards of living act. as a bait to lure them.
None of the assumption seem to be implicit because the reasons given in these assumptions have no mention in the
statement. Hence neither I nor II assumptions are implicit.
Ans. (d)
CHAPTER ELEVENSTATEMENTS AND ASSUMPTIONS
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