# Inequalities Quiz Set 033

### Question 1

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:

2. G ∧ 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: a

The statements can be translated to F < G = H = I. Conclusion I translates to F < I. Conclusion II translates to G = I. 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 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. λ means X < Y
5. © means X > Y

Conclusions:

3. V λ R

Which of the above conclusions is/are true?

A

both I and II.

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 > U(True)
2. S > U(True)
3. V < R(False)

### Question 3

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

1. Θ means X = Y
2. Ω means X ≯ (not more than) Y
3. \$ means X ≮ (not less than) Y
4. « means X < Y
5. η means X > Y

Statements: F Θ G; G « H; H η I;

Conclusions:

1. F Θ I
2. H η F
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 F = G < H > I. Conclusion I translates to F = I. Conclusion II translates to H > F. 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. λ means X = Y
2. ∅ means X ≤ Y
3. ∂ means X ≥ Y
4. Ξ means X < Y
5. ⊕ means X > Y

Statements: L ⊕ M; M λ N; N λ O; O ⊕ P;

Conclusions:

1. N Ξ P
2. O Ξ L
3. O Ξ M

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 L > M = N = O > P.

The conclusions translate to:

1. N < P(False)
2. O < L(True)
3. O < M(True)

### Question 5

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

1. Γ means X = Y
2. ∀ means X ≤ Y
3. Ω means X ≥ Y
4. © means X < Y
5. ∇ means X > Y

Statements: R ∇ S; S © T; T © U; U Γ V;

Conclusions:

1. T Γ V

Which of the above conclusions is/are true?

A

Neither of the three.

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. T = V(False)
2. R < U(False)
3. T < R(False) 