# Inequalities Quiz Set 035

### Question 1

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 2

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

1. Δ means X = Y
2. @ means X ≯ (not more than) Y
3. ⊗ means X ≥ Y
4. ® means X < Y
5. ∧ means X > Y

Statements: B ® C; C ® D; D Δ E;

Conclusions:

1. B ® D
2. D ∧ B
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 < D. Conclusion II translates to D > B. 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 3

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. ρ means X > Y

Statements: S ∩ T; T £ U; U ⊕ V;

Conclusions:

1. S ρ V
2. S £ 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: d

The statements can be translated to S ≤ T < U ≥ V. Conclusion I translates to S > V. Conclusion II translates to S < V. 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 4

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. ρ means X < Y
5. η means X > Y

Statements: J ¥ K; K % L; L ρ M;

Conclusions:

1. J η L
2. K ¥ 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 5

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

1. ρ means X = Y
2. η means X ≤ Y
3. Γ means X ≮ (not less than) Y
4. « means X < Y
5. Ω means X > Y

Statements: N Γ O; O Ω P; P η Q;

Conclusions:

1. O Ω Q
2. N Ω Q
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 N ≥ O > P ≤ Q. Conclusion I translates to O > Q. Conclusion II translates to N > Q. 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 ≥. 