# Inequalities Quiz Set 022

### Question 1

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

1. λ means X = Y
2. ∂ means X ≤ Y
3. © means X ≥ Y
4. Θ means X < Y
5. ∅ means X > Y

Statements: L λ M; M λ N; N ∅ O; O λ P;

Conclusions:

1. L Θ N
2. L ∅ O
3. M ∅ O

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to L = M = N > O = P.

The conclusions translate to:

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

### 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. Δ means X ≮ (not less than) Y
4. ρ means X < Y
5. ∇ means X > Y

Statements: O Δ P; P ® Q; Q § R;

Conclusions:

1. O ρ Q
2. O ∇ R
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 O ≥ P = Q ≤ R. Conclusion I translates to O < Q. Conclusion II translates to O > R. 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 ≯ (not more than) Y
3. Ω means X ≮ (not less than) Y
4. ∏ means X < Y
5. Δ means X > Y

Statements: Q Δ R; R ∩ S; S ∩ T;

Conclusions:

1. Q Δ T
2. R ∩ 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: a

The statements can be translated to Q > R = S = T. Conclusion I translates to Q > T. Conclusion II translates to R = T. 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. Ξ means X = Y
2. £ means X ≤ Y
3. ∇ means X ≥ Y
4. Ω means X < Y
5. ∩ means X > Y

Statements: I Ω J; J Ξ K; K ∩ L; L Ξ M;

Conclusions:

1. L ∩ I
2. K ∩ I
3. J ∩ L

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to I < J = K > L = M.

The conclusions translate to:

1. L > I(False)
2. K > I(True)
3. J > L(True)

### Question 5

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

1. ⊗ means X = Y
2. ω means X ≤ Y
3. § means X ≥ Y
4. Ξ means X < Y
5. η means X > Y

Statements: D ⊗ E; E ⊗ F; F Ξ G; G ⊗ H;

Conclusions:

1. D Ξ F
2. D Ξ H
3. F Ξ H

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 D = E = F < G = H.

The conclusions translate to:

1. D < F(False)
2. D < H(False)
3. F < H(True) 