Chapters

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Inequality

To solve inequality based questions, we must know about Inequality operator’s signs, they are:

 <, >, <=, >=,=

Let us discuss these symbols and their expiations:

To solve inequality based questions, we must know about Inequality operator’s signs, they are:

 <, >, <=, >=,=

Let us discuss these symbols and their expiations:

Symbol

Name

Example

Explanation

>

Greater than

A > B

  • A is greater than B
  • A is neither smaller tan nor equal to B

<

Less than

A < B

  • A is less than B
  • A is neither greater than nor equal to B

>=

Greater than and equal to

A >= B

  • A is greater or equal to B
  • A is not less than B

<=

Less than and equal to

A =< B

  • A is less than or equal to B
  • A is not greater than B

=

Equal to

A = B

  • A is equal to B
  • A is neither greater nor smaller than B

 

Checking if relations exist:

1). A > B > C: Yes there is a relation exist between A > C, since all the > sign are in the same direction.

2). A < B < C: Yes there is a relation exist between A < C, since all the < sign are in the same direction.

3). A > B < C: Indefinite relation or we can say no relation exist between A and C, since sign are in the opposite directions.

Q).With the help of statement find the conclusion which are followed by them

  1. If only conclusion I is true
  2. If only conclusion II is true
  3. If either conclusion I or II is true
  4. If neither conclusion I nor II is true
  5. If both conclusions I and II are true

 

Statements:

Q1)  C > D = E >= Y; F <= Y; A >= E

Conclusions:

  1. C > F
  2. A >= C

 

Answers 

According to the question, the whole relation will be

  1. C > D = E >= Y >= F           (True)

    Here, we can easily mover from C to F through open ends, Co this conclusion is true

  2. A >= E = D < C    (False)

    While going from A to C, path is closed after D due to apposite sign encountered, so we can’t go from A to C. Hence conclusion is False.

      (A) Is the answer, since only conclusion I is true.


Statements:

Q2)  L <= M < N > O >= P; U > N <= Q

Conclusions:

  1. U > L
  2. Q >= P

 

Answer

According to the question, the whole relation will be

  1. U > N > M >= L  (True)

    While going from U to L we always find open path, so conclusion I is always true.

  2. Q >= N > O >= P (True)

    While going from Q to P we always find open path, so conclusion II is always true.

(E) Is the answer, since both conclusion I and II are true.


Q3). What should be in place of (?). So that ‘Q > B’ as well as ‘U <=M’ definitely true?

                Q > M ? B >= O = U

(I)           <=           (II)          >             (III)         <             (IV)        >=           (V)          either <= or <

Ans). To find the path from Q to B, we must always find Open path, so according to question we must have open path. If we use (>=) then

         U =< M, will be definitely true.

So answer will be (IV)


Q4). P >= Q = M >= L >= N >= S, Find out P > S is true or false?

Ans. Let’s see some cases below:

  1. Here in this question we find an open path from P to S, so in first view this equation seems true
  2. But there is one more possibility can take place i.e. P = S. P can also be equal to S.

So the Relation P > S is false.


Q5). P >= Q = M >= L >= N >= S, Find out P = S is true or false?

Ans. As we have explained in above question we know that (P = S) and (P > S) both can be true. So we can’t establish the relationship P = S. Hence relation is indefinite i.e. False.


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