# Symbol notations inequalities questions

Symbols and Operations

Type 1 Symbols
1. In which of these expressions ‘S > V’ be definitely false?
A. S>P≥Q=G≥R>V
B. P<A≤S≤T; V≥O>T
C. V≤A≤L=R<S
D. S>C>=F≤H; V< F
E. S>T=O>=P; V<J=P

2. Which of the following symbols should be placed in the blank spaces respectively(in the same order from left to right) in order to complete the given expression in such a manner that both ‘D>R’ as well as ‘E≤B’ definitely holds true? B _ A _ R _ E _ D
A. >, ≥, <, = B. >, >, ≥, < C. ≥, ≥, ≥,≤
D. ≥, =, ≥,< E. Other than those given as options

Answers: B and D

Type 2
Direction: in each of the following questions, assuming the given statements to be true, find which of the following options holds
true:
Question 1
Statements: B < Q ≥ F < H, F = N Conclusions: I. N ≤ Q II. Q > H

Question 2
Statements: T ≥ Q, G < K, O ≤ M, G = J Conclusions: I. T ≥ O II. M > G

Solutions
1. It’s ‘If only conclusion I is true.’ Ans. A
2. It’s ‘If neither conclusion I nor conclusion
II is true’ Ans. D

Type 3
Directions to solve:
If,
i) A @ B means A is greater than B;
ii) A * B means A is either greater than or equal to B;
iii) A # B means A is equal to B;
iv) A \$ B means A is either smaller than or equal to B;
v) A + B means A is smaller than B.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is / are definitely True?

Give answer (a) if only conclusion I is true
Give answer (b) if only conclusion II is true
Give answer (c) if either conclusion I or II is true
Give answer (d) if neither conclusion I nor II is true.
Give answer (e) if both conclusions I and II are true.

Question 1
Statements :
P * Q; Q \$ R; S + T: R + S
Conclusions :
I. Q + S
II. Q + T
Options: a, b, c, d, e
Answer : option e.
Solution :
Given Statements: P * Q; Q \$ R; S + T; R + S
Converting the statements as follows:
P * Q => P is greater than or equal to Q; i.e., P > = Q
Q \$ R => Q is less than or equal to R; i.e., Q < = R
S + T => S is less than T; i.e., S < T
R + S => R is less than S; i.e., R < S

After conversion, combining the above, we have,
P > = Q < = R < S < T
From above inequality, we have, Q < = R < S < T
=> Q < S and Q < T
Given conclusions,
Q + S => Q < S which is true
Q + T => Q < T which is also true.
Hence, both conclusions I and II are true.

Question 2
Statements :
P + Q; R \$ S; T * Q; R @ P
Conclusions :
I. P \$ S
II. P + T
Options: a, b, c, d, e
Answer : option d.
Solution :
Given Statements: P + Q; R \$ S; T * Q; R @ P;
Converting the statements as follows:
P + Q => P < Q
R \$ S => R is less than or equal to S; i.e., R < = S
T * Q => T is greater than or equal to Q; i.e., T > = Q
R @ P => R > P
Combining the above four, we get, S > = R > P < Q < = T
From the above inequality, we have
S > P and P < T ….(1)
Given conclusions,
S \$ P => S < = P which is not true since S > P
P + T => P < T which is true.
Hence, conclusion II is true.

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