# Inequalities Quiz Set 011

### Question 1

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

1. ¢ means X = Y
2. ∅ means X ≤ Y
3. Γ means X ≮ (not less than) Y
4. @ means X < Y
5. ⊗ means X > Y

Statements: R ¢ S; S ⊗ T; T ⊗ U;

Conclusions:

1. S ¢ U
2. R ⊗ U
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 R = S > T > U. Conclusion I translates to S = U. Conclusion II translates to R > U. 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 2

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

1. % means X = Y
2. µ means X ≤ Y
3. Δ means X ≮ (not less than) Y
4. § means X < Y
5. √ means X > Y

Statements: B % C; C % D; D § E;

Conclusions:

1. B § E
2. C √ 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: c

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 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. ω means X = Y
2. Ξ means X ≯ (not more than) Y
3. ⊕ means X ≮ (not less than) Y
4. ® means X < Y
5. λ means X > Y

Statements: O ⊕ P; P ω Q; Q λ R;

Conclusions:

1. Q ω R
2. O λ R
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 O ≥ P = Q > R. Conclusion I translates to Q = R. Conclusion II translates to O > R. 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. Ξ means X ≯ (not more than) Y
3. ⊗ means X ≥ Y
4. £ means X < Y
5. ∃ means X > Y

Statements: B £ C; C ∃ D; D ω E;

Conclusions:

1. C ∃ E
2. D £ C
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 C > E. Conclusion II translates to D < C. 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 5

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

1. µ means X = Y
2. ® means X ≯ (not more than) Y
3. Γ means X ≥ Y
4. Θ means X < Y
5. \$ means X > Y

Statements: Q Θ R; R Θ S; S ® T;

Conclusions:

1. Q \$ T
2. S Θ 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 Q < R < S ≤ T. Conclusion I translates to Q > T. Conclusion II translates to S < 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 ≥. 