# Inequalities Quiz Set 040

### 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. η means X < Y
5. Δ means X > Y

Statements: D Δ E; E Δ F; F ® G;

Conclusions:

1. D Δ G
2. D Δ 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: a

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 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 2

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

1. ∃ means X = Y
2. ∧ means X ≤ Y
3. ρ means X ≥ Y
4. @ means X < Y
5. Γ means X > Y

Statements: B ∃ C; C ∃ D; D ρ E;

Conclusions:

1. B ∃ E
2. C Γ 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: d

The statements can be translated to B = C = D ≥ E. Conclusion I translates to B = E. Conclusion II translates to C > E. 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 3

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

1. Ω means X = Y
2. ∩ means X ≤ Y
3. Ξ means X ≥ Y
4. √ means X < Y
5. ∃ means X > Y

Statements: J ∃ K; K √ L; L Ω M; M √ N;

Conclusions:

1. K √ M
2. L √ J
3. M √ J

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 J > K < L = M < N.

The conclusions translate to:

1. K < M(True)
2. L < J(False)
3. M < J(False)

### Question 4

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

1. § means X = Y
2. ω means X ≤ Y
3. ρ means X ≮ (not less than) Y
4. λ means X < Y
5. Γ means X > Y

Statements: H ω I; I Γ J; J λ K;

Conclusions:

1. J λ K
2. J λ H
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 H ≤ I > J < K. Conclusion I translates to J < K. Conclusion II translates to J < H. 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 ≤ Y
3. ∧ means X ≮ (not less than) Y
4. Γ means X < Y
5. ∏ means X > Y

Statements: Q ∧ R; R ∏ S; S ⊕ T;

Conclusions:

1. Q Γ T
2. R ⊕ 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: a

The statements can be translated to Q ≥ R > S = T. Conclusion I translates to Q < T. Conclusion II translates to R = T. 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 ≥. 