# Inequalities Quiz Set 021

### Question 1

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

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

Statements: L ∩ M; M ≅ N; N ¢ O;

Conclusions:

1. L Ξ O
2. L ≅ 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: b

The statements can be translated to L ≤ M < N > O. Conclusion I translates to L = O. Conclusion II translates to L < N. 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 2

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

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

Statements: Q % R; R ∏ S; S Δ T; T Δ U;

Conclusions:

1. R ∏ T
2. S ∏ Q
3. Q ∏ U

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 Q = R > S < T < U.

The conclusions translate to:

1. R > T(False)
2. S > Q(False)
3. Q > U(False)

### Question 3

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. λ means X < Y
5. Δ means X > Y

Statements: J @ K; K ∑ L; L @ M;

Conclusions:

1. J ∑ L
2. J Δ K
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 J ≥ K = L ≥ M. Conclusion I translates to J = L. Conclusion II translates to J > K. 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 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: M ∧ N; N © O; O © P; P ∧ Q;

Conclusions:

1. N ∧ Q
2. M ∧ Q
3. M ∧ P

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 M > N = O = P > Q.

The conclusions translate to:

1. N > Q(True)
2. M > Q(True)
3. M > P(True)

### Question 5

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. µ means X > Y

Statements: G £ H; H £ I; I ∅ J; J £ K;

Conclusions:

1. J µ G
2. G £ I
3. I £ K

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 G = H = I < J = K.

The conclusions translate to:

1. J > G(True)
2. G = I(True)
3. I = K(False) 