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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 ≮ (not less than) Y
- ¥ means X < Y
- Ω means X > Y

**Statements: **S ∂ T; T ∂ U; U § V;

**Conclusions: **

- S ∂ V
- T Ω V

**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 S = T = U ≥ V. Conclusion I translates to S = V. Conclusion II translates to T > V. 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 2

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

- ∇ means X = Y
- $ means X ≤ Y
- ⊗ means X ≮ (not less than) Y
- Ξ means X < Y
- √ means X > Y

**Statements: **B ∇ C; C ∇ D; D ∇ E;

**Conclusions: **

- B ∇ D
- 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: a**

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

- µ means X = Y
- ∧ means X ≤ Y
- ∀ means X ≮ (not less than) Y
- Ξ means X < Y
- § means X > Y

**Statements: **N ∀ O; O § P; P § Q;

**Conclusions: **

- N µ Q
- N § 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: b**

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

- £ means X = Y
- ω means X ≤ Y
- ∂ means X ≥ Y
- ∏ means X < Y
- ⊗ means X > Y

**Statements: **A ∏ B; B £ C; C ⊗ D; D £ E;

**Conclusions: **

- A ∏ D
- B ⊗ E
- A £ C

Which of the above conclusions is/are true?

### Question 5

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

- ω means X = Y
- η means X ≯ (not more than) Y
- Γ means X ≮ (not less than) Y
- ¢ means X < Y
- µ means X > Y

**Statements: **N ¢ O; O µ P; P ω Q;

**Conclusions: **

- O µ Q
- P ¢ 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: a**

The statements can be translated to N < O > P = Q. Conclusion I translates to O > Q. Conclusion II translates to P < O. So we can see that both I and II are true.

This Blog Post/Article "Inequalities Quiz Set 003" 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