# Inequalities Quiz Set 050

### Question 1

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

1. ∀ means X = Y
2. @ means X ≯ (not more than) Y
3. Θ means X ≥ Y
4. § means X < Y
5. η means X > Y

Statements: M @ N; N η O; O @ P;

Conclusions:

1. M § P
2. N § O
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 M ≤ N > O ≤ P. Conclusion I translates to M < P. Conclusion II translates to N < O. 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. 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 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: 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: a

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 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 4

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 ≮ (not less than) Y
4. ∑ means X < Y
5. ≅ means X > Y

Statements: D @ E; E « F; F ∑ G;

Conclusions:

1. D ∑ G
2. E ≅ G
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 D ≤ E = F < G. Conclusion I translates to D < G. Conclusion II translates to E > G. 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 5

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

1. ¢ means X = Y
2. ⊗ means X ≯ (not more than) Y
3. η means X ≥ Y
4. « means X < Y
5. Θ means X > Y

Statements: M ⊗ N; N Θ O; O η P;

Conclusions:

1. O « M
2. M Θ O
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 M ≤ N > O ≥ P. Conclusion I translates to O < M. Conclusion II translates to M > O. 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 ≥.