# Inequalities Quiz Set 030

### 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. ∂ means X ≮ (not less than) Y
4. ∩ means X < Y
5. £ means X > Y

Statements: J ∂ K; K ≅ L; L £ M;

Conclusions:

1. L ≅ M
2. J £ M
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 J ≥ K = L > M. Conclusion I translates to L = M. Conclusion II translates to J > M. 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 2

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

1. Γ means X = Y
2. £ means X ≤ Y
3. √ means X ≥ Y
4. ≅ means X < Y
5. ® means X > Y

Statements: B Γ C; C ≅ D; D ≅ E; E ® F;

Conclusions:

1. F ® C
2. E ® B
3. B ≅ F

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 B = C < D < E > F.

The conclusions translate to:

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

### 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. ρ means X > Y

Statements: L § M; M ⊗ N; N \$ O;

Conclusions:

1. L ⊗ O
2. N ρ L
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 L ≤ M < N = O. Conclusion I translates to L < O. Conclusion II translates to N > L. 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. ω means X = Y
2. λ means X ≤ Y
3. Θ means X ≥ Y
4. ∅ means X < Y
5. ∩ means X > Y

Statements: T ∩ U; U ω V; V ∩ W;

Conclusions:

1. T ω W
2. U ∩ W
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 T > U = V > W. Conclusion I translates to T = W. Conclusion II translates to U > W. 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. λ means X = Y
2. µ means X ≯ (not more than) Y
3. ® means X ≥ Y
4. Γ means X < Y
5. © means X > Y

Statements: L ® M; M Γ N; N µ O;

Conclusions:

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 L ≥ M < N ≤ O. Conclusion I translates to M > O. Conclusion II translates to L > 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 ≥.