# Inequalities Quiz Set 017

### 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. ∧ means X > Y

Statements: S ∂ T; T ∂ U; U ∧ V; V « W;

Conclusions:

1. U ∧ S
2. S ∂ V
3. S ∂ W

Which of the above conclusions is/are true?

A

I only.

B

both I and II.

C

II only.

D

III only.

Soln.
Ans: a

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

The conclusions translate to:

1. U > S(True)
2. S < V(False)
3. S < W(False)

### Question 2

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

1. µ means X = Y
2. \$ means X ≤ Y
3. ® means X ≥ Y
4. % means X < Y
5. ∀ means X > Y

Statements: R µ S; S µ T; T ∀ U; U ∀ V;

Conclusions:

1. R µ T
2. U % S
3. R ∀ V

Which of the above conclusions is/are true?

A

both I and II.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to R = S = T > U > V.

The conclusions translate to:

1. R = T(True)
2. U < S(True)
3. R > V(False)

### Question 3

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

1. Θ means X = Y
2. ≅ means X ≯ (not more than) Y
3. Ξ means X ≥ Y
4. ∃ means X < Y
5. Δ means X > Y

Statements: N Θ O; O Θ P; P Θ Q;

Conclusions:

1. N Θ P
2. P Θ 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: a

The statements can be translated to N = O = P = Q. Conclusion I translates to N = P. Conclusion II translates to P = Q. 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 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. ¥ means X < Y
5. η means X > Y

Statements: C ¥ D; D η E; E ¢ F;

Conclusions:

1. E η F
2. E £ 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: d

The statements can be translated to C < D > E ≥ F. Conclusion I translates to E > F. Conclusion II translates to E = F. 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. η means X ≥ Y
4. @ means X < Y
5. Θ means X > Y

Statements: Q @ R; R ⊕ S; S @ T; T @ U;

Conclusions:

1. R @ U
2. S Θ U
3. R @ T

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to Q < R = S < T < U.

The conclusions translate to:

1. R < U(True)
2. S > U(False)
3. R < T(True)