# Inequalities Quiz Set 044

### Question 1

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: S § T; T ω U; U ω V; V ω W;

Conclusions:

1. T ω 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 S > T = U = V = W.

The conclusions translate to:

1. T = V(True)
2. W < T(True)
3. U < S(True)

### Question 2

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 3

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: F £ G; G ∩ H; H ¢ I;

Conclusions:

1. F \$ I
2. G \$ I
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 F < G = H ≤ I. Conclusion I translates to F > I. Conclusion II translates to G > I. 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 4

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

1. Γ means X = Y
2. ∅ means X ≯ (not more than) Y
3. η means X ≥ Y
4. Ω means X < Y
5. % means X > Y

Statements: M % N; N Γ O; O η P;

Conclusions:

1. N % P
2. N Γ 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: d

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

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:

2. D ∀ F
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 D ≤ E = F > G. Conclusion I translates to D = G. Conclusion II translates to D < F. 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 ≥.