# Inequalities Quiz Set 023

### Question 1

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

1. ω means X = Y
2. ® means X ≤ Y
3. ∇ means X ≥ Y
4. © means X < Y
5. § means X > Y

Statements: S § T; T ω U; U ω V; V ω W;

Conclusions:

1. T ω V

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 S > T = U = V = W.

The conclusions translate to:

1. T = V(True)
2. W < T(True)
3. U < S(True)

### Question 2

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 3

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

1. ω means X = Y
2. \$ means X ≤ Y
3. ® means X ≥ Y
4. µ means X < Y
5. ¥ means X > Y

Statements: S \$ T; T µ U; U ¥ V;

Conclusions:

1. S ω V
2. S µ 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 S ≤ T < U > V. Conclusion I translates to S = V. Conclusion II translates to S < 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 4

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 ≮ (not less than) Y
4. © means X < Y
5. \$ means X > Y

Statements: F § G; G \$ H; H ⊕ I;

Conclusions:

1. H § I
2. H \$ I
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 F = G > H ≥ I. Conclusion I translates to H = I. Conclusion II translates to H > I. 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 5

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

1. ∇ means X = Y
2. λ means X ≤ Y
3. ® means X ≥ Y
4. √ means X < Y
5. ¢ means X > Y

Statements: S λ T; T ¢ U; U ∇ V;

Conclusions:

1. T ¢ V
2. U √ 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 S ≤ T > U = V. Conclusion I translates to T > V. Conclusion II translates to U < 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 ≥.