# Inequalities Quiz Set 002

### Question 1

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

1. ⊕ means X = Y
2. ∅ means X ≤ Y
3. § means X ≥ Y
4. Ξ means X < Y
5. ∏ means X > Y

Statements: Q Ξ R; R Ξ S; S ⊕ T; T ∏ U;

Conclusions:

1. R Ξ U
2. R Ξ T
3. Q Ξ S

Which of the above conclusions is/are true?

A

both II and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to Q < R < S = T > U.

The conclusions translate to:

1. R < U(False)
2. R < T(True)
3. Q < S(True)

### Question 2

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

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

Statements: M ∑ N; N ¢ O; O µ P;

Conclusions:

1. O ∑ P
2. O ¢ P
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 M = N > O ≥ P. Conclusion I translates to O = P. Conclusion II translates to O > P. 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. Δ means X = Y
2. ® means X ≤ Y
3. © means X ≮ (not less than) Y
4. ∂ means X < Y
5. « means X > Y

Statements: B Δ C; C Δ D; D « E;

Conclusions:

1. B Δ 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: b

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 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. η means X = Y
2. £ means X ≤ Y
3. Θ means X ≮ (not less than) Y
4. ∩ means X < Y
5. ∇ means X > Y

Statements: B £ C; C η D; D ∇ E;

Conclusions:

1. B η E
2. B ∩ D
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 B ≤ C = D > E. Conclusion I translates to B = E. Conclusion II translates to B < D. 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 5

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 ≥ Y
4. Γ means X < Y
5. ≅ means X > Y

Statements: L ∀ M; M Γ N; N ≅ O;

Conclusions:

1. N ∏ O
2. N ≅ O
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 L ≥ M < N > O. Conclusion I translates to N = O. Conclusion II translates to N > O. 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 ≥.