# Inequalities Quiz Set 024

### Question 1

In a certain language different symbols represent different operators as follows.

1. ∃ means X = Y
2. % means X ≤ Y
3. Ω means X ≮ (not less than) Y
4. ⊗ means X < Y
5. £ means X > Y

Statements: N Ω O; O £ P; P ⊗ Q;

Conclusions:

1. N £ P
2. O Ω Q
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

either I or II can be true.

Soln.
Ans: c

The statements can be translated to N ≥ O > P < Q. Conclusion I translates to N > P. Conclusion II translates to O ≥ Q. So we can see that only conclusion I is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 2

In a certain language different symbols represent different operators as follows.

1. ∧ means X = Y
2. √ means X ≤ Y
3. ∩ means X ≥ Y
4. \$ means X < Y
5. ⊗ means X > Y

Statements: I \$ J; J ⊗ K; K √ L;

Conclusions:

1. I ⊗ K
2. I \$ L
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

neither I nor II is true.

Soln.
Ans: d

The statements can be translated to I < J > K ≤ L. Conclusion I translates to I > K. Conclusion II translates to I < L. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 3

In a certain language different symbols represent different operators as follows.

1. @ means X = Y
2. Ξ means X ≯ (not more than) Y
3. η means X ≮ (not less than) Y
4. ¢ means X < Y
5. ∃ means X > Y

Statements: F ¢ G; G @ H; H ∃ I;

Conclusions:

1. F ¢ I
2. G ∃ I
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

either I or II can be true.

Soln.
Ans: b

The statements can be translated to F < G = H > I. Conclusion I translates to F < I. Conclusion II translates to G > I. So we can see that only conclusion II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 4

In a certain language different symbols represent different operators as follows.

1. ® means X = Y
2. ρ means X ≤ Y
3. « means X ≮ (not less than) Y
4. ω means X < Y
5. ⊗ means X > Y

Statements: L ρ M; M ω N; N ρ O;

Conclusions:

1. L ⊗ N
2. O ω L
A

both I and II are true.

B

only conclusion II is true.

C

only conclusion I is true.

D

neither I nor II is true.

Soln.
Ans: d

The statements can be translated to L ≤ M < N ≤ O. Conclusion I translates to L > N. Conclusion II translates to O < L. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 5

In a certain language different symbols represent different operators as follows.

1. ∀ means X = Y
2. Γ means X ≤ Y
3. η means X ≥ Y
4. ∅ means X < Y
5. £ means X > Y

Statements: H £ I; I ∀ J; J ∅ K; K ∀ L;

Conclusions:

1. L £ I
2. I ∅ K
3. J £ H

Which of the above conclusions is/are true?

A

both I and II.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to H > I = J < K = L.

The conclusions translate to:

1. L > I(True)
2. I < K(True)
3. J > H(False) 