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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

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

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.

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.