# Inequalities Quiz Set 041

### Question 1

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

1. ∃ means X = Y
2. % means X ≤ Y
3. Ω means X ≮ (not less than) Y
4. ⊗ means X < Y
5. £ means X > Y

Statements: N Ω O; O £ P; P ⊗ Q;

Conclusions:

1. N £ P
2. O Ω Q
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 N ≥ O > P < Q. Conclusion I translates to N > P. Conclusion II translates to O ≥ Q. 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. λ means X = Y
2. ρ means X ≤ Y
3. ∀ means X ≥ Y
4. Θ means X < Y
5. ⊕ means X > Y

Statements: P Θ Q; Q λ R; R ⊕ S; S λ T;

Conclusions:

1. T ⊕ R
2. T ⊕ P
3. Q ⊕ T

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

The statements can be translated to P < Q = R > S = T.

The conclusions translate to:

1. T > R(False)
2. T > P(False)
3. Q > T(True)

### Question 3

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

1. ∏ means X = Y
2. ∂ means X ≯ (not more than) Y
3. ⊗ means X ≮ (not less than) Y
4. © means X < Y
5. ∩ means X > Y

Statements: D ∩ E; E © F; F ∂ G;

Conclusions:

2. E ∩ G
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 D > E < F ≤ G. Conclusion I translates to D < G. Conclusion II translates to E > G. 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 4

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

1. ® means X = Y
2. µ means X ≯ (not more than) Y
3. ¥ means X ≥ Y
4. ∅ means X < Y
5. ∧ means X > Y

Statements: L ¥ M; M ∅ N; N ¥ O;

Conclusions:

1. L ∅ O
2. O ∅ 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: d

The statements can be translated to L ≥ M < N ≥ O. Conclusion I translates to L < O. Conclusion II translates to O < L. 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. µ means X = Y
2. ⊕ means X ≯ (not more than) Y
3. ¥ means X ≮ (not less than) Y
4. ∏ means X < Y
5. √ means X > Y

Statements: O ¥ P; P µ Q; Q µ R;

Conclusions:

1. O √ R
2. P µ R
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 O ≥ P = Q = R. Conclusion I translates to O > R. Conclusion II translates to P = R. 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 ≥.