Inequalities Quiz Set 002

Question 1

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

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

Statements: O ⊗ P; P ⊗ Q; Q ⊗ R; R ⊗ S;

Conclusions:

1. P ⊗ S
2. S ∃ Q
3. Q ∃ O

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 O > P > Q > R > S.

The conclusions translate to:

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

Question 2

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

1. ρ means X = Y
2. @ means X ≤ Y
3. µ means X ≥ Y
4. ∅ means X < Y
5. ∑ means X > Y

Statements: K ∅ L; L ∅ M; M ρ N; N ρ O;

Conclusions:

1. L ∅ O
2. K ∅ O
3. K ∅ N

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 K < L < M = N = O.

The conclusions translate to:

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

Question 3

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

1. © means X = Y
2. £ means X ≤ Y
3. Δ means X ≥ Y
4. % means X < Y
5. µ means X > Y

Statements: M © N; N © O; O µ P; P µ Q;

Conclusions:

1. O µ M
2. Q % M
3. Q % O

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 M = N = O > P > Q.

The conclusions translate to:

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

Question 4

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

1. ® means X = Y
2. « means X ≤ Y
3. @ means X ≥ Y
4. λ means X < Y
5. √ means X > Y

Statements: J √ K; K ® L; L λ M; M λ N;

Conclusions:

1. L λ J
2. N λ J
3. M λ J

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 J > K = L < M < N.

The conclusions translate to:

1. L < J(False)
2. N < J(False)
3. M < J(False)

Question 5

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

1. § means X = Y
2. ¢ means X ≤ Y
3. Γ means X ≥ Y
4. ⊕ means X < Y
5. % means X > Y

Statements: T % U; U % V; V % W;

Conclusions:

1. T ⊕ V
2. U % W
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 T > U > V > W. Conclusion I translates to T < V. Conclusion II translates to U > W. 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 ≥. 