# Inequalities Quiz Set 008

### Question 1

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

1. √ means X = Y
2. % means X ≤ Y
3. Δ means X ≥ Y
4. ¥ means X < Y
5. ∑ means X > Y

Statements: E ¥ F; F √ G; G √ H; H √ I;

Conclusions:

1. H ∑ E
2. G ¥ I
3. E √ G

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 E < F = G = H = I.

The conclusions translate to:

1. H > E(True)
2. G < I(False)
3. E = G(False)

### 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. ⊗ means X < Y
5. ∀ means X > Y

Conclusions:

1. S ⊗ P
2. P ∀ T
3. R ⊗ P

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 P > Q = R = S = T.

The conclusions translate to:

1. S < P(True)
2. P > T(True)
3. R < P(True)

### Question 3

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

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

Statements: R √ S; S \$ T; T Δ U;

Conclusions:

1. R £ U
2. T \$ R
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 R = S < T ≤ U. Conclusion I translates to R > U. Conclusion II translates to T < R. 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. Ω means X = Y
2. Ξ means X ≤ Y
3. ρ means X ≥ Y
4. © means X < Y
5. Θ means X > Y

Statements: Q Ω R; R Ω S; S Θ T; T Ω U;

Conclusions:

2. R Θ U
3. Q Ω S

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 Q = R = S > T = U.

The conclusions translate to:

1. T < Q(True)
2. R > U(True)
3. Q = S(True)

### 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. η means X < Y
5. ∃ means X > Y

Statements: J § K; K ∃ L; L ∃ M; M § N;

Conclusions:

1. L ∃ J
2. J ∃ N
3. L ∃ N

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 J = K > L > M = N.

The conclusions translate to:

1. L > J(False)
2. J > N(True)
3. L > N(True) 