# Inequalities Quiz Set 027

### Question 1

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

1. ∂ means X = Y
2. ∧ means X ≤ Y
3. ∀ means X ≥ Y
4. ∃ means X < Y
5. Ξ means X > Y

Statements: F ∃ G; G ∃ H; H Ξ I; I Ξ J;

Conclusions:

1. H ∃ F
2. I Ξ G
3. J ∃ H

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

The statements can be translated to F < G < H > I > J.

The conclusions translate to:

1. H < F(False)
2. I > G(False)
3. J < H(True)

### Question 2

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

1. ∅ means X = Y
2. Γ 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 ∅ P
2. N « 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: b

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 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. Ξ means X ≤ Y
3. λ means X ≥ Y
4. ∑ means X < Y
5. ⊗ means X > Y

Statements: P ∑ Q; Q ∑ R; R ≅ S; S ≅ T;

Conclusions:

1. R ⊗ T
2. T ⊗ Q
3. P ∑ S

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 P < Q < R = S = T.

The conclusions translate to:

1. R > T(False)
2. T > Q(True)
3. P < S(True)

### Question 4

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: B ω C; C % D; D ω E;

Conclusions:

1. B % E
2. C % D
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 C < D. 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. Δ means X = Y
2. ∇ means X ≯ (not more than) Y
3. λ means X ≥ Y
4. £ means X < Y
5. ∂ means X > Y

Statements: B £ C; C £ D; D £ E;

Conclusions:

1. B £ D
2. C λ E
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 < D. Conclusion II translates to C ≥ E. 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 ≥. 