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### Question 1

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

- ∇ means X = Y
- Δ means X ≤ Y
- η means X ≥ Y
- @ means X < Y
- ρ means X > Y

**Statements: **B ρ C; C ρ D; D @ E; E ∇ F;

**Conclusions: **

- F ρ D
- C ρ F
- B ρ F

Which of the above conclusions is/are true?

### Question 2

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

- ∇ means X = Y
- ∂ means X ≯ (not more than) Y
- £ means X ≥ Y
- ∑ means X < Y
- ∃ means X > Y

**Statements: **G £ H; H ∃ I; I ∑ J;

**Conclusions: **

- G ∃ I
- H £ J

**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 G ≥ H > I < J. Conclusion I translates to G > I. Conclusion II translates to H ≥ J. 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 3

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

- ⊕ means X = Y
- ω means X ≯ (not more than) Y
- Δ means X ≥ Y
- µ means X < Y
- « means X > Y

**Statements: **M « N; N µ O; O Δ P;

**Conclusions: **

- O « P
- O ⊕ P

**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: d**

The statements can be translated to M > N < O ≥ P. Conclusion I translates to O > P. Conclusion II translates to O = P. So we can see that either I or II can be 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.

- Δ means X = Y
- ∧ means X ≤ Y
- £ means X ≮ (not less than) Y
- Ξ means X < Y
- Ω means X > Y

**Statements: **H ∧ I; I Ω J; J Ω K;

**Conclusions: **

- H Δ K
- 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.

- ⊕ means X = Y
- % means X ≤ Y
- ⊗ means X ≥ Y
- ω means X < Y
- ® means X > Y

**Statements: **G ⊕ H; H ® I; I ω J; J ω K;

**Conclusions: **

- K ω H
- J ω G
- I ω K

Which of the above conclusions is/are true?

This Blog Post/Article "Inequalities Quiz Set 029" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-10-26.