# Inequalities Quiz Set 026

### Question 1

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

1. ∏ means X = Y
2. η means X ≤ Y
3. Δ means X ≥ Y
4. √ means X < Y
5. Γ means X > Y

Statements: S η T; T √ U; U η V;

Conclusions:

1. S Γ U
2. V √ S
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 S ≤ T < U ≤ V. Conclusion I translates to S > U. Conclusion II translates to V < S. 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 2

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

1. ∑ means X = Y
2. Ω means X ≤ Y
3. ∃ means X ≥ Y
4. η means X < Y
5. ⊕ means X > Y

Statements: N ⊕ O; O ⊕ P; P η Q; Q η R;

Conclusions:

1. N ⊕ R
2. O η R
3. O ⊕ Q

Which of the above conclusions is/are true?

A

Neither of the three.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to N > O > P < Q < R.

The conclusions translate to:

1. N > R(False)
2. O < R(False)
3. O > Q(False)

### 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. Θ means X > Y

Statements: F ∧ G; G ⊕ H; H ∧ I; I ∧ J;

Conclusions:

1. J ⊕ H
2. F ⊕ J
3. G ⊕ I

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 F = G < H = I = J.

The conclusions translate to:

1. J < H(True)
2. F < J(True)
3. G < I(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. ρ means X ≥ Y
4. £ means X < Y
5. © means X > Y

Statements: M \$ N; N © O; O £ P;

Conclusions:

1. O £ P
2. O £ M
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 M ≤ N > O < P. Conclusion I translates to O < P. Conclusion II translates to O < M. 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 5

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

1. ⊗ means X = Y
2. η means X ≯ (not more than) Y
3. ∀ means X ≮ (not less than) Y
4. √ means X < Y
5. © means X > Y

Statements: F √ G; G ⊗ H; H √ I;

Conclusions:

1. F √ H
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: c

The statements can be translated to F < G = H < I. Conclusion I translates to F < H. Conclusion II translates to G ≥ I. 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 026" 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