# Inequalities Quiz Set 049

### 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. £ means X > Y

Statements: C ∀ D; D £ E; E © F; F © G;

Conclusions:

1. E £ G
2. G © C
3. G £ D

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 C = D > E < F < G.

The conclusions translate to:

1. E > G(False)
2. G < C(False)
3. G > D(False)

### Question 2

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)

### Question 3

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

1. Γ means X = Y
2. % means X ≯ (not more than) Y
3. √ means X ≥ Y
4. ∂ means X < Y
5. \$ means X > Y

Statements: L √ M; M ∂ N; N ∂ O;

Conclusions:

1. O \$ M
2. M √ O
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 L ≥ M < N < O. Conclusion I translates to O > M. Conclusion II translates to M ≥ O. 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 4

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

1. ∂ means X = Y
2. ρ means X ≤ Y
3. ∅ means X ≥ Y
4. Ξ means X < Y
5. Γ means X > Y

Statements: N ∂ O; O ∂ P; P ∂ Q; Q Γ R;

Conclusions:

1. N Γ P
2. R Ξ O
3. Q Ξ 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: c

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

The conclusions translate to:

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

### 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: A % B; B % C; C ⊗ D; D ⊗ E;

Conclusions:

1. E % C
2. C ∏ A
3. D ∏ A

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 A < B < C = D = E.

The conclusions translate to:

1. E < C(True)
2. C > A(True)
3. D > A(True) This Blog Post/Article "Inequalities Quiz Set 049" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-04-13