# Inequalities Quiz Set 047

### Question 1

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

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

Statements: L ⊕ M; M ≅ N; N λ O; O λ P;

Conclusions:

1. P λ L
2. N λ P
3. L λ N

Which of the above conclusions is/are true?

A

II only.

B

both I and II.

C

I only.

D

III only.

Soln.
Ans: a

The statements can be translated to L < M = N > O > P.

The conclusions translate to:

1. P > L(False)
2. N > P(True)
3. L > N(False)

### 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. ω means X ≥ Y
4. ∑ means X < Y
5. ∂ means X > Y

Statements: B ∑ C; C ∑ D; D ∂ E;

Conclusions:

1. B ∑ E
2. D ∂ B
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 B < C < D > E. Conclusion I translates to B < E. Conclusion II translates to D > B. 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. ∩ 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. J ¥ H
2. H ¢ J
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 H ≤ I > J ≥ K. Conclusion I translates to J < H. Conclusion II translates to H > J. 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 4

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

1. ∧ means X = Y
2. ∃ means X ≯ (not more than) Y
3. ω means X ≥ Y
4. § means X < Y
5. ∩ means X > Y

Statements: M ∩ N; N § O; O ∧ P;

Conclusions:

1. M ∩ N
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: a

The statements can be translated to M > N < O = P. Conclusion I translates to M > N. Conclusion II translates to N < P. 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 5

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

1. ⊗ means X = Y
2. Ξ means X ≤ Y
3. ∏ means X ≮ (not less than) Y
4. ∃ means X < Y
5. µ means X > Y

Statements: B Ξ C; C ∃ D; D ∃ E;

Conclusions:

1. B ∃ E
2. D ⊗ B
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 B ≤ C < D < E. Conclusion I translates to B < E. Conclusion II translates to D = B. 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 ≥. 