# Inequalities Quiz Set 038

### Question 1

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

1. ∂ means X = Y
2. ∏ means X ≤ Y
3. Ξ means X ≥ Y
4. √ means X < Y
5. ∇ means X > Y

Statements: T ∇ U; U ∂ V; V √ W;

Conclusions:

1. T ∇ V
2. U Ξ 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 ≥.

### Question 2

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

1. Θ means X = Y
2. ⊗ means X ≯ (not more than) Y
3. ∀ means X ≮ (not less than) Y
4. ∧ means X < Y
5. Δ means X > Y

Statements: N ∧ O; O Δ P; P ⊗ Q;

Conclusions:

1. N Δ P
2. N ∧ Q
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 N < O > P ≤ Q. Conclusion I translates to N > P. Conclusion II translates to N < Q. 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. ≅ means X ≤ Y
3. ¢ means X ≥ Y
4. η means X < Y
5. ∏ means X > Y

Statements: I η J; J ∏ K; K η L;

Conclusions:

1. I η J
2. J η L
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 I < J > K < L. Conclusion I translates to I < J. Conclusion II translates to J < L. 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 4

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: J ⊗ K; K ⊗ L; L ∩ M; M ∩ N;

Conclusions:

1. M % K
2. N ∩ L
3. J ∩ M

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to J = K = L > M > N.

The conclusions translate to:

1. M < K(True)
2. N > L(False)
3. J > M(True)

### Question 5

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

1. √ means X = Y
2. λ 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. F ∇ H
2. G ∇ E
3. D \$ H

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 D < E < F > G < H.

The conclusions translate to:

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