# Inequalities Quiz Set 050

### Question 1

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. µ means X > Y

Statements: Q ¥ R; R ∅ S; S ∅ T;

Conclusions:

1. R ∅ T
2. Q ≅ S
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: a

The statements can be translated to Q ≤ R = S = T. Conclusion I translates to R = T. Conclusion II translates to Q < S. So we can see that both I and II are 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 ≯ (not more than) Y
3. Γ means X ≮ (not less than) Y
4. « means X < Y
5. ¥ means X > Y

Statements: J Γ K; K « L; L ¢ M;

Conclusions:

1. K « M
2. L ¢ 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: a

The statements can be translated to J ≥ K < L = M. Conclusion I translates to K < M. Conclusion II translates to L = M. So we can see that both I and II are 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. ω means X = Y
2. µ means X ≤ Y
3. ∏ means X ≥ Y
4. Δ means X < Y
5. ® means X > Y

Statements: E Δ F; F ω G; G Δ H; H Δ I;

Conclusions:

1. F Δ H
2. I ® G
3. E Δ G

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 E < F = G < H < I.

The conclusions translate to:

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

### Question 4

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. ω means X > Y

Statements: H ⊗ I; I ∧ J; J £ K;

Conclusions:

1. H ω K
2. H ∧ 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 H ≤ I < J ≥ K. Conclusion I translates to H > K. Conclusion II translates to H < 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 5

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

1. λ means X = Y
2. ® means X ≤ Y
3. Ω means X ≥ Y
4. ∀ means X < Y
5. « means X > Y

Statements: G λ H; H λ I; I « J; J « K;

Conclusions:

1. G « J
2. K ∀ H
3. K ∀ 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 G = H = I > J > K.

The conclusions translate to:

1. G > J(True)
2. K < H(True)
3. K < I(True) 