# Inequalities Quiz Set 041

### Question 1

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

1. η means X = Y
2. ω means X ≤ Y
3. Ω means X ≥ Y
4. % means X < Y
5. ∧ means X > Y

Statements: A ∧ B; B η C; C ∧ D; D η E;

Conclusions:

1. C ∧ E
2. E % A
3. A ∧ C

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 A > B = C > D = E.

The conclusions translate to:

1. C > E(True)
2. E < A(True)
3. A > C(True)

### Question 2

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

1. @ means X = Y
2. ∑ means X ≤ Y
3. ω means X ≥ Y
4. § means X < Y
5. ® means X > Y

Statements: J § K; K @ L; L § M;

Conclusions:

1. J § L
2. K ω 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: c

The statements can be translated to J < K = L < M. Conclusion I translates to J < L. Conclusion II translates to K ≥ M. 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 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: 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 ≥.

### Question 4

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

1. Ω means X = Y
2. ∑ means X ≯ (not more than) Y
3. ⊕ means X ≮ (not less than) Y
4. ∇ means X < Y
5. Δ means X > Y

Statements: F Ω G; G Δ H; H ∑ I;

Conclusions:

1. F Δ I
2. H ∇ F
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 H < F. 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 5

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

1. « means X = Y
2. Γ means X ≯ (not more than) Y
3. ⊗ means X ≥ Y
4. ∧ means X < Y
5. η means X > Y

Statements: B ∧ C; C ∧ D; D ⊗ E;

Conclusions:

1. D η E
2. D « 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 D > E. Conclusion II translates to D = 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 ≥. 