# Inequalities Quiz Set 039

### Question 1

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

1. λ means X = Y
2. ∇ means X ≤ Y
3. ¥ means X ≥ Y
4. ⊕ means X < Y
5. √ means X > Y

Statements: S √ T; T √ U; U √ V; V λ W;

Conclusions:

1. W ⊕ U
2. W ⊕ S
3. V ⊕ S

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 S > T > U > V = W.

The conclusions translate to:

1. W < U(True)
2. W < S(True)
3. V < S(True)

### Question 2

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: K ¢ L; L @ M; M ¢ N; N ¢ O;

Conclusions:

1. K § M
2. K @ N
3. N § L

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

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

The conclusions translate to:

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

### Question 3

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

1. Ξ means X = Y
2. µ means X ≤ Y
3. ¢ means X ≥ Y
4. Θ means X < Y
5. Γ means X > Y

Statements: H Γ I; I Γ J; J Θ K; K Θ L;

Conclusions:

1. I Γ K
2. L Θ I
3. L Θ J

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 H > I > J < K < L.

The conclusions translate to:

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

### Question 4

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

1. ∀ means X = Y
2. λ means X ≤ Y
3. Γ means X ≮ (not less than) Y
4. √ means X < Y
5. § means X > Y

Statements: L λ M; M ∀ N; N Γ O;

Conclusions:

1. M § O
2. N ∀ O
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 L ≤ M = N ≥ O. Conclusion I translates to M > O. Conclusion II translates to N = O. 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 5

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

1. ¢ means X = Y
2. § means X ≤ Y
3. ⊗ means X ≮ (not less than) Y
4. ∩ means X < Y
5. Γ means X > Y

Statements: S ¢ T; T ∩ U; U ∩ V;

Conclusions:

1. S ∩ U
2. T Γ V
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 S = T < U < V. Conclusion I translates to S < U. Conclusion II translates to T > V. 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 ≥.