# Inequalities Quiz Set 020

### 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. ρ means X ≥ Y
4. ∩ means X < Y
5. ® means X > Y

Statements: G ® H; H ∩ I; I @ J;

Conclusions:

1. G ® H
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: a

The statements can be translated to G > H < I = J. Conclusion I translates to G > H. Conclusion II translates to H < J. 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 2

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

1. £ means X = Y
2. η means X ≤ Y
3. © means X ≥ Y
4. Θ means X < Y
5. ω means X > Y

Statements: N Θ O; O Θ P; P £ Q; Q Θ R;

Conclusions:

1. O Θ R
2. R Θ P
3. P ω N

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 N < O < P = Q < R.

The conclusions translate to:

1. O < R(True)
2. R < P(False)
3. P > N(True)

### 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. ⊕ means X ≮ (not less than) Y
4. ® means X < Y
5. Θ means X > Y

Statements: F ∀ G; G Θ H; H ∀ I;

Conclusions:

1. F Θ H
2. I ® G
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 F = G > H = I. Conclusion I translates to F > H. Conclusion II translates to I < G. 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. ω means X = Y
2. ρ means X ≤ Y
3. λ means X ≥ Y
4. ∂ means X < Y
5. ∀ means X > Y

Statements: K ω L; L ω M; M ∀ N; N ∀ O;

Conclusions:

1. K ω M
2. O ∂ K
3. N ∂ L

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 K = L = M > N > O.

The conclusions translate to:

1. K = M(True)
2. O < K(False)
3. N < L(True)

### Question 5

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

1. ¢ means X = Y
2. Ω means X ≯ (not more than) Y
3. ∀ means X ≮ (not less than) Y
4. £ means X < Y
5. § means X > Y

Statements: Q £ R; R § S; S ∀ T;

Conclusions:

1. S § T
2. S ¢ 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: d

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