# Inequalities Quiz Set 029

### Question 1

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

1. ∇ means X = Y
2. Δ means X ≤ Y
3. η means X ≥ Y
4. @ means X < Y
5. ρ means X > Y

Statements: B ρ C; C ρ D; D @ E; E ∇ F;

Conclusions:

1. F ρ D
2. C ρ F
3. B ρ F

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 B > C > D < E = F.

The conclusions translate to:

1. F > D(True)
2. C > F(False)
3. B > F(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 ≥ Y
4. ∑ means X < Y
5. ∃ means X > Y

Statements: G £ H; H ∃ I; I ∑ J;

Conclusions:

1. G ∃ I
2. H £ J
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 G ≥ H > I < J. Conclusion I translates to G > I. Conclusion II translates to H ≥ J. 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 3

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

1. ⊕ means X = Y
2. ω means X ≯ (not more than) Y
3. Δ means X ≥ Y
4. µ means X < Y
5. « means X > Y

Statements: M « N; N µ O; O Δ P;

Conclusions:

1. O « P
2. O ⊕ 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: d

The statements can be translated to M > N < O ≥ P. Conclusion I translates to O > P. Conclusion II translates to O = P. 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. Δ means X = Y
2. ∧ means X ≤ Y
3. £ means X ≮ (not less than) Y
4. Ξ means X < Y
5. Ω means X > Y

Statements: H ∧ I; I Ω J; J Ω K;

Conclusions:

1. H Δ K
2. I Ω K
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 H ≤ I > J > K. Conclusion I translates to H = K. Conclusion II translates to I > K. 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 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. ω means X < Y
5. ® means X > Y

Statements: G ⊕ H; H ® I; I ω J; J ω K;

Conclusions:

1. K ω H
2. J ω G
3. I ω K

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

The statements can be translated to G = H > I < J < K.

The conclusions translate to:

1. K < H(False)
2. J < G(False)
3. I < K(True)