# Inequalities Quiz Set 028

### 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. ¢ means X ≥ Y
4. ω means X < Y
5. µ means X > Y

Statements: G ¢ H; H µ I; I ¥ J;

Conclusions:

1. H µ J
2. G µ J
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 G ≥ H > I ≤ J. Conclusion I translates to H > J. Conclusion II translates to G > J. 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. @ means X = Y
2. £ means X ≤ Y
3. \$ means X ≥ Y
4. © means X < Y
5. ∀ means X > Y

Statements: F @ G; G @ H; H © I; I ∀ J;

Conclusions:

1. J ∀ G
3. I ∀ F

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 F = G = H < I > J.

The conclusions translate to:

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

### Question 3

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

1. µ means X = Y
2. ¢ means X ≤ Y
3. ∧ means X ≥ Y
4. © means X < Y
5. ρ means X > Y

Statements: N © O; O µ P; P ρ Q; Q ρ R;

Conclusions:

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 N < O = P > Q > R.

The conclusions translate to:

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

### Question 4

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. @ means X > Y

Statements: D @ E; E ∇ F; F ¥ G;

Conclusions:

1. F @ G
2. F ® 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: d

The statements can be translated to D > E < F ≥ G. Conclusion I translates to F > G. Conclusion II translates to F = G. 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 5

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

1. ⊗ means X = Y
2. ρ means X ≤ Y
3. ¥ means X ≥ Y
4. ∃ means X < Y
5. Δ means X > Y

Statements: L ⊗ M; M ⊗ N; N ⊗ O; O ⊗ P;

Conclusions:

1. P ∃ N
2. O ∃ M
3. M ⊗ P

Which of the above conclusions is/are false?

A

All.

B

both I and II.

C

II only.

D

both II and III.

Soln.
Ans: b

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

The conclusions translate to:

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