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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
- ρ means X < Y
- µ means X > Y

**Statements: **O µ P; P µ Q; Q « R; R « S;

**Conclusions: **

- S ρ P
- O ρ Q
- O µ S

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 ≤ Y
- © means X ≮ (not less than) Y
- ρ means X < Y
- Ω means X > Y

**Statements: **Q © R; R ρ S; S ρ T;

**Conclusions: **

- T Ω R
- R © T

**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 Q ≥ R < S < T. Conclusion I translates to T > R. Conclusion II translates to R ≥ T. 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
- ρ means X ≤ Y
- $ means X ≮ (not less than) Y
- η means X < Y
- © means X > Y

**Statements: **R ¥ S; S © T; T η U;

**Conclusions: **

- R © T
- T η U

**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 R = S > T < U. Conclusion I translates to R > T. Conclusion II translates to T < U. 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 4

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

- ∃ means X = Y
- ⊕ means X ≤ Y
- « means X ≥ Y
- √ means X < Y
- ω means X > Y

**Statements: **M ω N; N ω O; O √ P; P √ Q;

**Conclusions: **

- N √ Q
- Q ω O
- O ω M

Which of the above conclusions is/are true?

### Question 5

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

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

**Statements: **M √ N; N ⊕ O; O λ P;

**Conclusions: **

- M ⊕ P
- O ∇ M

**A**

both I and II are true.

**B**

only conclusion II is true.

**C**

only conclusion I is true.

**D**

neither I nor II is true.

**Soln.**

**Ans: d**

The statements can be translated to M = N > O ≤ P. Conclusion I translates to M > P. Conclusion II translates to O < M. So we can see that neither I nor II 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 045" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.