# Inequalities Quiz Set 037

### Question 1

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

1. √ means X = Y
2. η means X ≤ Y
3. Γ means X ≥ Y
4. £ means X < Y
5. ¢ means X > Y

Statements: H √ I; I £ J; J ¢ K; K ¢ L;

Conclusions:

1. I ¢ L
2. H £ L
3. I £ K

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 H = I < J > K > L.

The conclusions translate to:

1. I > L(False)
2. H < L(False)
3. I < K(False)

### 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. ∏ means X < Y
5. Ω means X > Y

Statements: F ® G; G ∏ H; H £ I;

Conclusions:

1. F Ω I
2. H ∏ F
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 F = G < H ≤ I. Conclusion I translates to F > I. Conclusion II translates to H < F. 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 3

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. Δ means X > Y

Statements: C % D; D % E; E ∏ F; F ∏ G;

Conclusions:

1. C % E
2. F Δ C
3. D % G

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 C < D < E = F = G.

The conclusions translate to:

1. C < E(True)
2. F > C(True)
3. D < G(True)

### 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. ∩ means X > Y

Statements: B ∩ C; C ∂ D; D ∩ E; E ∩ F;

Conclusions:

1. D ∂ B
2. B ∩ F
3. E ∩ C

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

### Question 5

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: J © K; K ∅ L; L ∧ M;

Conclusions:

1. K √ M
2. K ∅ M
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 J < K = L ≥ M. Conclusion I translates to K > M. Conclusion II translates to K = M. 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 ≥. 