# Inequalities Quiz Set 031

### 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. £ means X < Y
5. ∏ means X > Y

Statements: N © O; O © P; P ∏ Q; Q £ R;

Conclusions:

1. O ∏ Q
2. O ∏ R
3. R £ P

Which of the above conclusions is/are true?

A

I only.

B

both I and II.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to N = O = P > Q < R.

The conclusions translate to:

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

### Question 2

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

1. λ means X = Y
2. % means X ≯ (not more than) Y
3. µ means X ≥ Y
4. ρ means X < Y
5. ∧ means X > Y

Statements: O % P; P λ Q; Q ρ R;

Conclusions:

1. O ρ R
2. P ∧ 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: c

The statements can be translated to O ≤ P = Q < R. Conclusion I translates to O < R. Conclusion II translates to P > R. 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. § means X = Y
2. ∇ means X ≤ Y
3. ⊕ means X ≥ Y
4. ¥ means X < Y
5. % means X > Y

Statements: N % O; O % P; P ¥ Q; Q § R;

Conclusions:

1. Q ¥ O
2. P ¥ R
3. R ¥ N

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 N > O > P < Q = R.

The conclusions translate to:

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

### Question 4

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

1. ∅ means X = Y
2. Γ means X ≯ (not more than) Y
3. Ω means X ≥ Y
4. « means X < Y
5. ∩ means X > Y

Statements: M ∩ N; N « O; O ∩ P;

Conclusions:

1. M ∅ P
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 M > N < O > P. Conclusion I translates to M = P. 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 ≥.

### Question 5

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

1. ⊕ means X = Y
2. « means X ≤ Y
3. ∧ means X ≮ (not less than) Y
4. Γ means X < Y
5. ∏ means X > Y

Statements: Q ∧ R; R ∏ S; S ⊕ T;

Conclusions:

1. Q Γ T
2. R ⊕ T
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 Q ≥ R > S = T. Conclusion I translates to Q < T. Conclusion II translates to R = T. 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 ≥.