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### Question 1

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

- ∂ means X = Y
- ∧ means X ≤ Y
- ∀ means X ≥ Y
- ∃ means X < Y
- Ξ means X > Y

**Statements: **F ∃ G; G ∃ H; H Ξ I; I Ξ J;

**Conclusions: **

- H ∃ F
- I Ξ G
- J ∃ H

Which of the above conclusions is/are true?

### Question 2

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

- ∅ means X = Y
- Γ means X ≯ (not more than) Y
- Ω means X ≥ Y
- « means X < Y
- ∩ means X > Y

**Statements: **M ∩ N; N « O; O ∩ P;

**Conclusions: **

- M ∅ P
- 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 M > N < O > P. Conclusion I translates to M = P. 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 3

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

- ≅ means X = Y
- Ξ means X ≤ Y
- λ means X ≥ Y
- ∑ means X < Y
- ⊗ means X > Y

**Statements: **P ∑ Q; Q ∑ R; R ≅ S; S ≅ T;

**Conclusions: **

- R ⊗ T
- T ⊗ Q
- P ∑ S

Which of the above conclusions is/are true?

### Question 4

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

- ω means X = Y
- ∏ means X ≤ Y
- ∑ means X ≥ Y
- % means X < Y
- ⊗ means X > Y

**Statements: **B ω C; C % D; D ω E;

**Conclusions: **

- B % E
- C % D

**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 B = C < D = E. Conclusion I translates to B < E. Conclusion II translates to C < D. 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 5

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

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

**Statements: **B £ C; C £ D; D £ E;

**Conclusions: **

- B £ D
- C λ E

**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 B < C < D < E. Conclusion I translates to B < D. Conclusion II translates to C ≥ E. 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 ≥.

This Blog Post/Article "Inequalities Quiz Set 027" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.