# Inequalities Quiz Set 001

### Question 1

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

1. Θ means X = Y
2. η means X ≯ (not more than) Y
3. ∏ means X ≥ Y
4. « means X < Y
5. ⊕ means X > Y

Statements: G ∏ H; H ⊕ I; I Θ J;

Conclusions:

1. G « J
2. H Θ 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: a

The statements can be translated to G ≥ H > I = J. Conclusion I translates to G < J. Conclusion II translates to H = J. 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 ≯ (not more than) Y
3. © means X ≮ (not less than) Y
4. Ξ means X < Y
5. ∃ means X > Y

Statements: F Ξ G; G ∏ H; H © I;

Conclusions:

1. G ∃ I
2. G ∏ I
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 F < G = H ≥ I. Conclusion I translates to G > I. Conclusion II translates to G = I. 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 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: N ⊗ O; O ≅ P; P ≅ Q;

Conclusions:

1. N ⊗ Q
2. O ≅ 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: b

The statements can be translated to N < O > P > Q. Conclusion I translates to N < Q. Conclusion II translates to O > Q. 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. ∀ means X = Y
2. ∧ means X ≤ Y
3. © means X ≥ Y
4. Δ means X < Y
5. Γ means X > Y

Statements: B ∀ C; C ∀ D; D ∧ E;

Conclusions:

1. B Γ E
2. D Γ B
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 B = C = D ≤ E. Conclusion I translates to B > E. Conclusion II translates to D > B. 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. λ means X = Y
2. ∃ means X ≤ Y
3. ∩ means X ≥ Y
4. ¢ means X < Y
5. ∅ means X > Y

Statements: T ¢ U; U ¢ V; V ∅ W; W ¢ X;

Conclusions:

1. W ∅ U
2. V ∅ X
3. X ∅ T

Which of the above conclusions is/are true?

A

Neither of the three.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to T < U < V > W < X.

The conclusions translate to:

1. W > U(False)
2. V > X(False)
3. X > T(False) 