**Download Handout 1 on Symbols and Operations – Must do 60 EASY questions>>****Download Handout 2 Symbol inequalities questions – Must do 36 MEDIUM 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.