# Inequalities Quiz Set 007

### 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. ⊗ means X > Y

Statements: B ∃ C; C ∃ D; D ⊗ E; E ∃ F;

Conclusions:

1. D ⊗ B
2. E ⊗ C
3. D ⊗ F

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 B < C < D > E < F.

The conclusions translate to:

1. D > B(True)
2. E > C(False)
3. D > F(False)

### Question 2

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: T ∀ U; U Ω V; V Ω W; W Ω X;

Conclusions:

1. T ∀ X
2. U Ω X
3. T ∀ V

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 T > U = V = W = X.

The conclusions translate to:

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

### Question 3

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

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

Statements: Q ∧ R; R ∧ S; S @ T;

Conclusions:

1. S § T
2. S Θ 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: d

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 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. \$ means X ≥ Y
4. ∅ means X < Y
5. ∃ means X > Y

Statements: M ≅ N; N ∃ O; O ∃ P;

Conclusions:

1. M √ 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: b

The statements can be translated to M ≤ N > O > P. Conclusion I translates to M = P. Conclusion II translates to N > P. 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. ≅ means X = Y
2. ∂ means X ≤ Y
3. ® means X ≮ (not less than) Y
4. ∃ means X < Y
5. £ means X > Y

Statements: K £ L; L £ M; M ∃ N;

Conclusions:

1. K ∃ M
2. L £ N
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 K > L > M < N. Conclusion I translates to K < M. Conclusion II translates to L > N. 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 ≥.