# Inequalities Quiz Set 004

### Question 1

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. ∅ means X > Y

Statements: P ∅ Q; Q ∅ R; R ∅ S; S ∀ T;

Conclusions:

1. T ∀ Q
2. R ∀ P
3. T ∀ R

Which of the above conclusions is/are true?

A

II only.

B

both I and II.

C

I only.

D

III only.

Soln.
Ans: a

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

The conclusions translate to:

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

### Question 2

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

1. ® means X = Y
2. Ξ means X ≤ Y
3. ⊕ means X ≮ (not less than) Y
4. Θ means X < Y
5. ⊗ means X > Y

Statements: Q ⊕ R; R Θ S; S Ξ T;

Conclusions:

1. R ⊗ T
2. Q ⊗ T
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 R > T. Conclusion II translates to Q > T. 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 3

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

1. η means X = Y
2. ¥ means X ≯ (not more than) Y
3. ⊕ means X ≥ Y
4. \$ means X < Y
5. √ means X > Y

Statements: M ⊕ N; N η O; O η P;

Conclusions:

1. M √ P
2. N η 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: a

The statements can be translated to M ≥ N = O = P. Conclusion I translates to M > P. Conclusion II translates to N = P. 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 4

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

1. ≅ means X = Y
2. Ξ means X ≤ Y
3. λ means X ≥ Y
4. ∑ means X < Y
5. ⊗ means X > Y

Statements: P ∑ Q; Q ∑ R; R ≅ S; S ≅ T;

Conclusions:

1. R ⊗ T
2. T ⊗ Q
3. P ∑ 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 P < Q < R = S = T.

The conclusions translate to:

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

### 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: B λ C; C \$ D; D \$ E;

Conclusions:

1. B \$ D
2. C Ξ 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 < D. 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 ≥.