# Inequalities Quiz Set 013

### Question 1

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 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. Δ means X < Y
5. @ means X > Y

Statements: K @ L; L @ M; M ∏ N;

Conclusions:

1. K Δ N
2. M @ K
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 K > L > M ≤ N. Conclusion I translates to K < N. Conclusion II translates to M > K. 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 3

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

1. % means X = Y
2. Θ means X ≤ Y
3. « means X ≮ (not less than) Y
4. ⊕ means X < Y
5. ∃ means X > Y

Statements: M % N; N ∃ O; O ∃ P;

Conclusions:

1. N % P
2. M ∃ 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: b

The statements can be translated to M = N > O > P. Conclusion I translates to N = P. Conclusion II translates to M > P. 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 4

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 ≥.

### 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: K ∩ L; L µ M; M ∩ N; N ∩ O;

Conclusions:

1. O « K
2. L µ O
3. K « M

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 K = L > M = N = O.

The conclusions translate to:

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