Page 1
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 

< 
Less than 
A < B 

>= 
Greater than and equal to 
A >= B 

<= 
Less than and equal to 
A =< B 

= 
Equal to 
A = 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
 If only conclusion I is true
 If only conclusion II is true
 If either conclusion I or II is true
 If neither conclusion I nor II is true
 If both conclusions I and II are true
Statements:
Q1) C > D = E >= Y; F <= Y; A >= E
Conclusions:
 C > F
 A >= C
Answers
According to the question, the whole relation will be
 C > D = E >= Y >= F (True)
Here, we can easily mover from C to F through open ends, Co this conclusion is true
 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:
 U > L
 Q >= P
Answer
According to the question, the whole relation will be
 U > N > M >= L (True)
While going from U to L we always find open path, so conclusion I is always true.
 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:
 Here in this question we find an open path from P to S, so in first view this equation seems true
 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.