# Inequalities Quiz Set 004

### Question 1

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

1. @ means X = Y
2. ∅ means X ≤ Y
3. © means X ≮ (not less than) Y
4. ⊗ means X < Y
5. « means X > Y

Statements: H ∅ I; I « J; J @ K;

Conclusions:

1. I « K
2. J ⊗ 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: a

The statements can be translated to H ≤ I > J = K. Conclusion I translates to I > K. Conclusion II translates to J < I. 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 2

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

1. ∃ means X = Y
2. ∩ means X ≤ Y
3. Ω means X ≮ (not less than) Y
4. ∇ means X < Y
5. ρ means X > Y

Statements: Q Ω R; R ∇ S; S ρ T;

Conclusions:

1. S ∃ T
2. S ρ 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: b

The statements can be translated to Q ≥ R < S > T. Conclusion I translates to S = T. Conclusion II translates to S > T. 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 3

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

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

Statements: G Δ H; H © I; I © J; J Δ K;

Conclusions:

1. J Δ H
2. K Δ I

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 G < H > I > J < K.

The conclusions translate to:

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

### Question 4

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

1. « means X = Y
2. @ means X ≤ Y
3. Δ means X ≮ (not less than) Y
4. % means X < Y
5. λ means X > Y

Statements: Q Δ R; R % S; S Δ T;

Conclusions:

1. Q % T
2. T % Q
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 Q ≥ R < S ≥ T. Conclusion I translates to Q < T. Conclusion II translates to T < Q. 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. Ω means X = Y
2. ∇ means X ≤ Y
3. ∅ means X ≥ Y
4. Θ means X < Y
5. ∏ means X > Y

Statements: A ∏ B; B ∏ C; C ∏ D; D ∏ E;

Conclusions:

1. C ∏ E
2. C ∏ A
3. E Θ B

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to A > B > C > D > E.

The conclusions translate to:

1. C > E(True)
2. C > A(False)
3. E < B(True) 