Inequalities Quiz Set 048

Question 1

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

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

Statements: D Ω E; E ∃ F; F Ω G; G Ω H;

Conclusions:

1. F Ω D
2. E Ω G
3. H Ξ E

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 D > E = F > G > H.

The conclusions translate to:

1. F > D(False)
2. E > G(True)
3. H < E(True)

Question 2

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

1. « means X = Y
2. § means X ≤ Y
3. ρ means X ≥ Y
4. ∑ means X < Y
5. ∏ means X > Y

Statements: O ∑ P; P « Q; Q ∏ R; R « S;

Conclusions:

1. O ∑ S
2. P ∏ R
3. Q ∑ S

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 O < P = Q > R = S.

The conclusions translate to:

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

Question 3

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 ≥ Y
4. Γ means X < Y
5. ≅ means X > Y

Statements: L ∀ M; M Γ N; N ≅ O;

Conclusions:

1. N ∏ O
2. N ≅ 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: b

The statements can be translated to L ≥ M < N > O. Conclusion I translates to N = O. Conclusion II translates to N > O. 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. η means X = Y
2. ∀ means X ≤ Y
3. ∃ means X ≥ Y
4. ∧ means X < Y
5. Γ means X > Y

Statements: I η J; J ∧ K; K Γ L; L Γ M;

Conclusions:

1. J ∧ L
2. M Γ I
3. K ∧ M

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 I = J < K > L > M.

The conclusions translate to:

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

Question 5

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

1. ® means X = Y
2. µ means X ≤ Y
3. ≅ means X ≥ Y
4. ∧ means X < Y
5. ∂ means X > Y

Statements: D ® E; E ∧ F; F ∂ G; G ∂ H;

Conclusions:

1. G ∂ D
2. E ∧ H
3. G ∂ E

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 D = E < F > G > H.

The conclusions translate to:

1. G > D(False)
2. E < H(False)
3. G > E(False) This Blog Post/Article "Inequalities Quiz Set 048" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.