# Inequalities Quiz Set 003

### 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. ¥ means X < Y
5. Ω means X > Y

Statements: S ∂ T; T ∂ U; U § V;

Conclusions:

1. S ∂ V
2. T Ω V
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 S = T = U ≥ V. Conclusion I translates to S = V. Conclusion II translates to T > V. 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. Ξ means X < Y
5. √ means X > Y

Statements: B ∇ C; C ∇ D; D ∇ E;

Conclusions:

1. B ∇ D
2. D ∇ E
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 B = C = D = E. Conclusion I translates to B = D. Conclusion II translates to D = E. 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. µ means X = Y
2. ∧ means X ≤ Y
3. ∀ means X ≮ (not less than) Y
4. Ξ means X < Y
5. § means X > Y

Statements: N ∀ O; O § P; P § Q;

Conclusions:

1. N µ Q
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: b

The statements can be translated to N ≥ O > P > Q. Conclusion I translates to N = Q. Conclusion II translates to N > 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. £ means X = Y
2. ω means X ≤ Y
3. ∂ means X ≥ Y
4. ∏ means X < Y
5. ⊗ means X > Y

Statements: A ∏ B; B £ C; C ⊗ D; D £ E;

Conclusions:

1. A ∏ D
2. B ⊗ E
3. A £ C

Which of the above conclusions is/are true?

A

II only.

B

both I and II.

C

I only.

D

III only.

Soln.
Ans: a

The statements can be translated to A < B = C > D = E.

The conclusions translate to:

1. A < D(False)
2. B > E(True)
3. A = C(False)

### Question 5

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

1. ω means X = Y
2. η means X ≯ (not more than) Y
3. Γ means X ≮ (not less than) Y
4. ¢ means X < Y
5. µ means X > Y

Statements: N ¢ O; O µ P; P ω Q;

Conclusions:

1. O µ Q
2. P ¢ O
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 N < O > P = Q. Conclusion I translates to O > Q. Conclusion II translates to P < O. 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 ≥. 