# Inequalities Quiz Set 019

### Question 1

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

1. η means X = Y
2. £ means X ≤ Y
3. Θ means X ≮ (not less than) Y
4. ∩ means X < Y
5. ∇ means X > Y

Statements: B £ C; C η D; D ∇ E;

Conclusions:

1. B η E
2. B ∩ D
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 B ≤ C = D > E. Conclusion I translates to B = E. Conclusion II translates to B < D. 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 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. ω means X > Y

Statements: C ω D; D ∏ E; E ∏ F;

Conclusions:

1. C ω F
2. D ∏ F
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 C > D = E = F. Conclusion I translates to C > F. Conclusion II translates to D = F. 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. @ means X = Y
2. ∂ means X ≯ (not more than) Y
3. Γ means X ≥ Y
4. ⊕ means X < Y
5. ∑ means X > Y

Statements: G ∑ H; H ⊕ I; I ⊕ J;

Conclusions:

1. H ⊕ J
2. H Γ J
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 G > H < I < J. Conclusion I translates to H < J. Conclusion II translates to H ≥ J. 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. Ξ means X ≤ Y
3. ⊕ means X ≮ (not less than) Y
4. Θ means X < Y
5. ⊗ means X > Y

Statements: Q ⊕ R; R Θ S; S Ξ T;

Conclusions:

1. R ⊗ T
2. Q ⊗ 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 Q ≥ R < S ≤ T. Conclusion I translates to R > T. Conclusion II translates to Q > 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 5

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

1. Δ means X = Y
2. ∂ means X ≤ Y
3. § means X ≥ Y
4. ¢ means X < Y
5. λ means X > Y

Statements: T λ U; U λ V; V § W;

Conclusions:

1. V λ W
2. V Δ W
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 T > U > V ≥ W. Conclusion I translates to V > W. Conclusion II translates to V = W. 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 ≥. 