Inequalities Quiz Set 005

Question 1

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

1. ω means X = Y
2. ∩ means X ≤ Y
3. ∑ means X ≥ Y
4. λ means X < Y
5. Δ means X > Y

Statements: T λ U; U λ V; V ω W; W ω X;

Conclusions:

1. U λ X
2. V ω X
3. T λ V

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 T < U < V = W = X.

The conclusions translate to:

1. U < X(True)
2. V = X(True)
3. T < V(True)

Question 2

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

1. λ means X = Y
2. % means X ≯ (not more than) Y
3. µ means X ≥ Y
4. ρ means X < Y
5. ∧ means X > Y

Statements: O % P; P λ Q; Q ρ R;

Conclusions:

1. O ρ R
2. P ∧ R
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 O ≤ P = Q < R. Conclusion I translates to O < R. Conclusion II translates to P > R. 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. ∀ means X ≤ Y
3. ∏ means X ≥ Y
4. Θ means X < Y
5. ® means X > Y

Statements: F Θ G; G ® H; H ∃ I; I ∃ J;

Conclusions:

1. I Θ G
2. F Θ J
3. J Θ H

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: b

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

The conclusions translate to:

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

Question 4

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

1. Θ 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 Θ I; I ∅ J;

Conclusions:

1. G ∇ J
2. F ∅ H
3. J ∅ H

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 F < G < H = I > J.

The conclusions translate to:

1. G < J(False)
2. F > H(False)
3. J > H(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: N © O; O © P; P ∏ Q; Q £ R;

Conclusions:

1. O ∏ Q
2. O ∏ R
3. R £ P

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 N = O = P > Q < R.

The conclusions translate to:

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