# Inequalities Quiz Set 031

### Question 1

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: T µ U; U \$ V; V √ W;

Conclusions:

1. T ∏ W
2. V µ T
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 T > U = V ≤ W. Conclusion I translates to T < W. Conclusion II translates to V > T. 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 2

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: J © K; K ∃ L; L ∇ M;

Conclusions:

1. J % M
2. K % M
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 J < K = L ≤ M. Conclusion I translates to J > M. Conclusion II translates to K > M. 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. \$ means X ≯ (not more than) Y
3. ≅ means X ≮ (not less than) Y
4. § means X < Y
5. Θ means X > Y

Statements: Q Θ R; R @ S; S § T;

Conclusions:

1. Q Θ S
2. R ≅ T
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 Q > R = S < T. Conclusion I translates to Q > S. Conclusion II translates to R ≥ T. 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 4

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

1. ∧ means X = Y
2. Ω means X ≯ (not more than) Y
3. ∏ means X ≮ (not less than) Y
4. ∩ means X < Y
5. µ means X > Y

Statements: O ∏ P; P ∧ Q; Q ∏ R;

Conclusions:

1. O ∧ Q
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: d

The statements can be translated to O ≥ P = Q ≥ R. Conclusion I translates to O = Q. Conclusion II translates to O > 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 5

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. Ξ means X > Y

Statements: S ∩ T; T ∅ U; U ∩ V;

Conclusions:

1. S ∅ V
2. T ∅ U
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 S = T < U = V. Conclusion I translates to S < V. Conclusion II translates to T < U. 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 ≥.