# Inequalities Quiz Set 015

### 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. Ξ means X < Y
5. % means X > Y

Statements: M Ξ N; N ∧ O; O ∧ P;

Conclusions:

1. M Ξ P
2. N ∧ P
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 M < N = O = P. Conclusion I translates to M < P. Conclusion II translates to N = P. 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 ≤ Y
3. ∏ means X ≮ (not less than) Y
4. µ means X < Y
5. ⊗ means X > Y

Statements: M \$ N; N ⊗ O; O µ P;

Conclusions:

1. M ⊗ O
2. O µ P
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 M = N > O < P. Conclusion I translates to M > O. Conclusion II translates to O < P. 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 3

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

1. Γ means X = Y
2. ∅ means X ≯ (not more than) Y
3. η means X ≥ Y
4. Ω means X < Y
5. % means X > Y

Statements: M % N; N Γ O; O η P;

Conclusions:

1. N % P
2. N Γ P
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 M > N = O ≥ P. Conclusion I translates to N > P. Conclusion II translates to N = P. 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. ρ means X ≯ (not more than) Y
3. ¥ means X ≥ Y
4. ∑ means X < Y
5. ω means X > Y

Statements: M ω N; N ∑ O; O ρ P;

Conclusions:

1. M ∑ P
2. N ω P
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 M > N < O ≤ P. Conclusion I translates to M < P. Conclusion II translates to N > P. 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 5

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

1. £ means X = Y
2. ® means X ≤ Y
3. Θ means X ≮ (not less than) Y
4. @ means X < Y
5. ¢ means X > Y

Statements: R £ S; S ¢ T; T £ U;

Conclusions:

1. R ¢ T
2. U @ 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 R = S > T = U. Conclusion I translates to R > T. Conclusion II translates to U < 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 ≥. 