# Inequalities Quiz Set 005

### 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. ω means X > Y

Statements: C ω D; D ∏ E; E ∏ F;

Conclusions:

1. C ω F
2. D ∏ 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: a

The statements can be translated to C > D = E = F. Conclusion I translates to C > F. Conclusion II translates to D = F. 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. µ means X = Y
2. \$ means X ≤ Y
3. ® means X ≥ Y
4. % means X < Y
5. ∀ means X > Y

Statements: R µ S; S µ T; T ∀ U; U ∀ V;

Conclusions:

1. R µ T
2. U % S
3. R ∀ V

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

### Question 3

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

1. Ω means X = Y
2. ∑ means X ≯ (not more than) Y
3. ⊕ means X ≮ (not less than) Y
4. ∇ means X < Y
5. Δ means X > Y

Statements: F Ω G; G Δ H; H ∑ I;

Conclusions:

1. F Δ I
2. H ∇ F
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 F = G > H ≤ I. Conclusion I translates to F > I. Conclusion II translates to H < F. 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 4

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

1. Δ means X = Y
2. ∧ means X ≤ Y
3. £ means X ≮ (not less than) Y
4. Ξ means X < Y
5. Ω means X > Y

Statements: H ∧ I; I Ω J; J Ω K;

Conclusions:

1. H Δ K
2. I Ω K
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 H ≤ I > J > K. Conclusion I translates to H = K. Conclusion II translates to I > K. 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. λ means X ≥ Y
4. η means X < Y
5. % means X > Y

Statements: I § J; J % K; K % L; L § M;

Conclusions:

1. M η I
2. J % M
3. L η I

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 I = J > K > L = M.

The conclusions translate to:

1. M < I(True)
2. J > M(True)
3. L < I(True)