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### Question 1

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: **M ≅ N; N ∃ O; O ∃ P;

**Conclusions: **

- M √ P
- 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 M ≤ N > O > P. Conclusion I translates to M = P. 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 2

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

- Ξ means X = Y
- ∩ means X ≤ Y
- ⊗ means X ≮ (not less than) Y
- ≅ means X < Y
- ¢ means X > Y

**Statements: **L ∩ M; M ≅ N; N ¢ O;

**Conclusions: **

- L Ξ O
- L ≅ N

**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 L ≤ M < N > O. Conclusion I translates to L = O. Conclusion II translates to L < N. 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
- ≅ means X ≤ Y
- ¢ means X ≥ Y
- η means X < Y
- ∏ means X > Y

**Statements: **I η J; J ∏ K; K η L;

**Conclusions: **

- I η J
- J η L

**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 I < J > K < L. Conclusion I translates to I < J. Conclusion II translates to J < L. 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
- ∇ means X > Y

**Statements: **L ∇ M; M ∇ N; N @ O; O @ P;

**Conclusions: **

- M ∇ O
- L ∇ O
- P ∇ N

Which of the above conclusions is/are true?

### Question 5

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

- £ means X = Y
- ∩ means X ≤ Y
- Ξ means X ≥ Y
- « means X < Y
- ∀ means X > Y

**Statements: **R ∀ S; S ∀ T; T « U; U ∀ V;

**Conclusions: **

- V ∀ T
- R ∀ U
- U « S

Which of the above conclusions is/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 2017-04-07.