# Inequalities Quiz Set 037

### Question 1

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

1. § means X = Y
2. ω means X ≤ Y
3. % means X ≮ (not less than) Y
4. ∏ means X < Y
5. ® means X > Y

Statements: B § C; C § D; D ω E;

Conclusions:

1. B ® E
2. D ® B
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 B = C = D ≤ E. Conclusion I translates to B > E. Conclusion II translates to D > B. 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 2

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

1. « means X = Y
2. \$ means X ≤ Y
3. ≅ means X ≥ Y
4. ρ means X < Y
5. µ means X > Y

Statements: O µ P; P µ Q; Q « R; R « S;

Conclusions:

1. S ρ P
2. O ρ Q
3. O µ S

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

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

The conclusions translate to:

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

### 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: B © C; C © D; D ⊕ E; E ⊕ F;

Conclusions:

1. F ∏ C

Which of the above conclusions is/are true?

A

All.

B

both I and II.

C

II only.

D

both II and III.

Soln.
Ans: a

The statements can be translated to B < C < D = E = F.

The conclusions translate to:

1. F > C(True)
2. B < D(True)
3. B < F(True)

### Question 4

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

1. Δ means X = Y
2. ∇ means X ≯ (not more than) Y
3. λ means X ≥ Y
4. £ means X < Y
5. ∂ means X > Y

Statements: B £ C; C £ D; D £ E;

Conclusions:

1. B £ D
2. C λ 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 ≥.

### Question 5

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: R £ S; S ∧ T; T ∧ U; U ∧ V;

Conclusions:

1. R £ V
2. R § T
3. S ∧ V

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

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

The conclusions translate to:

1. R < V(True)
2. R > T(False)
3. S = V(True)