# Inequalities Quiz Set 016

### Question 1

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

1. Γ means X = Y
2. η means X ≯ (not more than) Y
3. © means X ≮ (not less than) Y
4. √ means X < Y
5. ∅ means X > Y

Statements: D η E; E Γ F; F η G;

Conclusions:

1. D ∅ F
2. G √ D
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 D ≤ E = F ≤ G. Conclusion I translates to D > F. Conclusion II translates to G < D. 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 2

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

1. Γ means X = Y
2. ∇ means X ≤ Y
3. % means X ≥ Y
4. ∏ means X < Y
5. ∂ means X > Y

Statements: B Γ C; C Γ D; D ∏ E; E Γ F;

Conclusions:

1. F ∂ D
2. B ∏ E
3. B ∂ D

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 B = C = D < E = F.

The conclusions translate to:

1. F > D(True)
2. B < E(True)
3. B > D(False)

### Question 3

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

1. \$ means X = Y
2. Θ means X ≤ Y
3. λ means X ≮ (not less than) Y
4. Ω means X < Y
5. ∀ means X > Y

Statements: R \$ S; S Ω T; T λ U;

Conclusions:

1. T \$ U
2. T ∀ U
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 R = S < T ≥ U. Conclusion I translates to T = U. Conclusion II translates to T > U. 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 4

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

1. ≅ means X = Y
2. Γ means X ≤ Y
3. η means X ≥ Y
4. ∇ means X < Y
5. µ means X > Y

Statements: T µ U; U µ V; V Γ W;

Conclusions:

1. T ∇ W
2. V µ 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 T > U > V ≤ W. Conclusion I translates to T < W. Conclusion II translates to V > 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. ∃ means X = Y
2. ∅ means X ≤ Y
3. Ω means X ≥ Y
4. @ means X < Y
5. ω means X > Y

Statements: B ω C; C @ D; D ω E; E ω F;

Conclusions:

1. C @ F
2. B ω D
3. D @ F

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 B > C < D > E > F.

The conclusions translate to:

1. C < F(False)
2. B > D(False)
3. D < F(False)