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### Question 1

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

- Ξ means X = Y
- © means X ≤ Y
- @ means X ≥ Y
- ∧ means X < Y
- ∃ means X > Y

**Statements: **J ∧ K; K Ξ L; L ∃ M;

**Conclusions: **

- J ∧ M
- K ∃ M

**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 J < K = L > M. Conclusion I translates to J < M. Conclusion II translates to K > M. 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 2

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

- η means X = Y
- ¥ means X ≯ (not more than) Y
- ⊕ means X ≥ Y
- $ means X < Y
- √ means X > Y

**Statements: **M ⊕ N; N η O; O η P;

**Conclusions: **

- M √ P
- N η 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: a**

The statements can be translated to M ≥ N = O = P. Conclusion I translates to M > P. Conclusion II translates to N = P. 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 3

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

- ρ means X = Y
- § means X ≤ Y
- ∏ means X ≥ Y
- © means X < Y
- ¢ means X > Y

**Statements: **F ρ G; G © H; H ¢ I; I ρ J;

**Conclusions: **

- I ¢ G
- F © J
- H ρ J

Which of the above conclusions is/are true?

### Question 4

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

- £ means X = Y
- $ means X ≤ Y
- ∧ means X ≮ (not less than) Y
- Θ means X < Y
- ≅ means X > Y

**Statements: **B $ C; C £ D; D ∧ E;

**Conclusions: **

- C ≅ E
- D £ 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: d**

The statements can be translated to B ≤ C = D ≥ E. Conclusion I translates to C > E. Conclusion II translates to D = E. 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 5

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

- ∩ means X = Y
- ≅ means X ≯ (not more than) Y
- ∏ means X ≮ (not less than) Y
- @ means X < Y
- Γ means X > Y

**Statements: **N @ O; O Γ P; P @ Q;

**Conclusions: **

- N @ O
- O @ Q

**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 N < O > P < Q. Conclusion I translates to N < O. Conclusion II translates to O < Q. So we can see that only conclusion I is true.

This Blog Post/Article "Inequalities Quiz Set 025" 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