# Inequalities Quiz Set 018

### Question 1

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: P ¢ Q; Q ¢ R; R ⊗ S; S ∩ T;

Conclusions:

1. Q ⊗ S
2. S ∩ P
3. T ∩ P

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 P = Q = R > S < T.

The conclusions translate to:

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

### 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. η means X > Y

Statements: T ® U; U ® V; V η W; W η X;

Conclusions:

1. X ® V
2. U η X
3. T ® X

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 T < U < V > W > X.

The conclusions translate to:

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

### Question 3

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

1. Δ means X = Y
2. √ means X ≤ Y
3. \$ means X ≥ Y
4. ∩ means X < Y
5. © means X > Y

Statements: H ∩ I; I © J; J ∩ K; K ∩ L;

Conclusions:

1. K ∩ I
2. H ∩ L
3. K ∩ 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 H < I > J < K < L.

The conclusions translate to:

1. K < I(False)
2. H < L(False)
3. K < H(False)

### Question 4

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

1. ≅ means X = Y
2. Δ means X ≯ (not more than) Y
3. ¥ means X ≥ Y
4. \$ means X < Y
5. © means X > Y

Conclusions:

1. G ≅ J
2. H \$ I
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 G > H < I > J. Conclusion I translates to G = J. Conclusion II translates to H < I. 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 ≥.

### Question 5

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. ∂ means X < Y
5. ¥ means X > Y

Statements: M ∂ N; N ω O; O ¥ P; P ω Q;

Conclusions:

1. O ¥ M
2. O ¥ Q
3. N ¥ P

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 M < N = O > P = Q.

The conclusions translate to:

1. O > M(True)
2. O > Q(True)
3. N > P(True) 