# Inequalities Quiz Set 026

### Question 1

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 ≥.

### Question 2

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

1. ∑ means X = Y
2. Ω means X ≤ Y
3. ® means X ≮ (not less than) Y
4. Θ means X < Y
5. @ means X > Y

Statements: L Ω M; M Θ N; N Θ O;

Conclusions:

1. L Θ O
2. N ∑ 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: c

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 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. Θ means X = Y
2. Ω means X ≯ (not more than) Y
3. \$ means X ≮ (not less than) Y
4. « means X < Y
5. η means X > Y

Statements: F Θ G; G « H; H η I;

Conclusions:

1. F Θ I
2. H η 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 F = G < H > I. Conclusion I translates to F = I. Conclusion II translates to H > 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. η means X ≯ (not more than) Y
3. ∏ means X ≮ (not less than) Y
4. ρ means X < Y
5. √ means X > Y

Statements: F Ω G; G ρ H; H ∏ I;

Conclusions:

1. H Ω I
2. H √ I
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 F = G < H ≥ I. Conclusion I translates to H = I. Conclusion II translates to H > I. 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. λ means X = Y
2. « means X ≤ Y
3. ∀ means X ≥ Y
4. \$ means X < Y
5. Ξ means X > Y

Statements: T Ξ U; U Ξ V; V λ W;

Conclusions:

1. T Ξ W
2. T Ξ V
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 T > U > V = W. Conclusion I translates to T > W. Conclusion II translates to T > V. 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 ≥.