# Inequalities Quiz Set 044

### Question 1

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 ≥ 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: c

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 I 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. ρ 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: R ∂ S; S ρ T; T ρ U;

Conclusions:

1. S ρ U
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: a

The statements can be translated to R ≤ S = T = U. Conclusion I translates to S = U. Conclusion II translates to R < T. 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. 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 ¥ E
2. A ¥ D
3. A ¥ C

Which of the above conclusions is/are true?

A

All.

B

both I and II.

C

II only.

D

both II and III.

Soln.
Ans: a

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

The conclusions translate to:

1. A > E(True)
2. A > D(True)
3. A > C(True)

### Question 4

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. Ξ means X > Y

Statements: T Ξ U; U Ξ V; V λ W;

Conclusions:

1. T Ξ W
2. T Ξ 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: a

The statements can be translated to T > U > V = W. Conclusion I translates to T > W. Conclusion II translates to T > V. 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. Δ means X = Y
2. √ means X ≯ (not more than) Y
3. ρ means X ≮ (not less than) Y
4. ® means X < Y
5. ∏ means X > Y

Statements: Q ∏ R; R Δ S; S ∏ T;

Conclusions:

1. Q Δ T
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: b

The statements can be translated to Q > R = S > T. Conclusion I translates to Q = T. Conclusion II translates to R > T. 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 ≥. 