# Inequalities Quiz Set 032

### Question 1

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

1. λ means X = Y
2. ρ means X ≤ Y
3. ∀ means X ≥ Y
4. Θ means X < Y
5. ⊕ means X > Y

Statements: P Θ Q; Q λ R; R ⊕ S; S λ T;

Conclusions:

1. T ⊕ R
2. T ⊕ P
3. Q ⊕ T

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

The statements can be translated to P < Q = R > S = T.

The conclusions translate to:

1. T > R(False)
2. T > P(False)
3. Q > T(True)

### Question 2

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

1. ω means X = Y
2. Δ means X ≤ Y
3. @ means X ≮ (not less than) Y
4. ∅ means X < Y
5. Ω means X > Y

Statements: K Ω L; L Ω M; M @ N;

Conclusions:

1. M Ω N
2. M ω N
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: d

The statements can be translated to K > L > M ≥ N. Conclusion I translates to M > N. Conclusion II translates to M = N. So we can see that either I or II can be 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. ¢ means X ≤ Y
3. ∩ means X ≥ Y
4. « means X < Y
5. @ means X > Y

Statements: D « E; E « F; F \$ G; G \$ H;

Conclusions:

1. H @ D
2. D « G
3. E « H

Which of the above conclusions is/are true?

A

All.

B

both I and II.

C

II only.

D

both II and III.

Soln.
Ans: a

The statements can be translated to D < E < F = G = H.

The conclusions translate to:

1. H > D(True)
2. D < G(True)
3. E < H(True)

### Question 4

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

1. ∏ means X = Y
2. ∂ means X ≯ (not more than) Y
3. ⊗ means X ≮ (not less than) Y
4. © means X < Y
5. ∩ means X > Y

Statements: D ∩ E; E © F; F ∂ G;

Conclusions:

1. D © G
2. E ∩ G
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 D > E < F ≤ G. Conclusion I translates to D < G. Conclusion II translates to E > G. 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. η means X = Y
2. Ω means X ≤ Y
3. ¢ means X ≥ Y
4. ∩ means X < Y
5. ω means X > Y

Statements: T ω U; U ω V; V ∩ W;

Conclusions:

1. T ∩ V
2. U ω W
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 T > U > V < W. Conclusion I translates to T < V. Conclusion II translates to U > W. 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 ≥. This Blog Post/Article "Inequalities Quiz Set 032" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-04-13