# Inequalities Quiz Set 006

### Question 1

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

1. ∧ means X = Y
2. ρ means X ≤ Y
3. ∑ means X ≮ (not less than) Y
4. Θ means X < Y
5. ¥ means X > Y

Statements: B ρ C; C ∧ D; D ρ E;

Conclusions:

1. B ¥ D
2. E Θ B
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 B ≤ C = D ≤ E. Conclusion I translates to B > D. Conclusion II translates to E < B. 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 ≯ (not more than) Y
3. § means X ≥ Y
4. % means X < Y
5. √ means X > Y

Statements: M √ N; N % O; O % P;

Conclusions:

1. N % P
2. N § P
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 M > N < O < P. Conclusion I translates to N < P. Conclusion II translates to N ≥ P. 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. Θ means X ≤ Y
3. ∂ means X ≥ Y
4. ⊗ means X < Y
5. Δ means X > Y

Statements: H ⊗ I; I ⊗ J; J ∧ K; K ⊗ L;

Conclusions:

1. K Δ I
2. J ⊗ H
3. H ⊗ L

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 H < I < J = K < L.

The conclusions translate to:

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

### Question 4

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

1. ∏ means X = Y
2. λ means X ≤ Y
3. ∂ means X ≥ Y
4. Γ means X < Y
5. ≅ means X > Y

Statements: R Γ S; S Γ T; T ∏ U; U ∏ V;

Conclusions:

1. T ≅ V
2. R Γ U
3. R Γ V

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to R < S < T = U = V.

The conclusions translate to:

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

### Question 5

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

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

Statements: I λ J; J λ K; K ∃ L; L ∃ M;

Conclusions:

1. I ⊗ K
2. J λ L
3. I λ M

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to I > J > K = L = M.

The conclusions translate to:

1. I < K(False)
2. J > L(True)
3. I > M(True)