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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
- µ means X > Y

**Statements: **Q ¥ R; R ∅ S; S ∅ T;

**Conclusions: **

- R ∅ T
- Q ≅ S

**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 Q ≤ R = S = T. Conclusion I translates to R = T. Conclusion II translates to Q < S. 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 2

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

- ¢ means X = Y
- √ means X ≯ (not more than) Y
- Γ means X ≮ (not less than) Y
- « means X < Y
- ¥ means X > Y

**Statements: **J Γ K; K « L; L ¢ M;

**Conclusions: **

- K « M
- L ¢ 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: a**

The statements can be translated to J ≥ K < L = M. Conclusion I translates to K < M. Conclusion II translates to L = M. 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.

- ω means X = Y
- µ means X ≤ Y
- ∏ means X ≥ Y
- Δ means X < Y
- ® means X > Y

**Statements: **E Δ F; F ω G; G Δ H; H Δ I;

**Conclusions: **

- F Δ H
- I ® G
- E Δ G

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
- ∧ means X < Y
- ω means X > Y

**Statements: **H ⊗ I; I ∧ J; J £ K;

**Conclusions: **

- H ω K
- H ∧ K

**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 H ≤ I < J ≥ K. Conclusion I translates to H > K. Conclusion II translates to H < K. 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.

- λ means X = Y
- ® means X ≤ Y
- Ω means X ≥ Y
- ∀ means X < Y
- « means X > Y

**Statements: **G λ H; H λ I; I « J; J « K;

**Conclusions: **

- G « J
- K ∀ H
- K ∀ I

Which of the above conclusions is/are true?

This Blog Post/Article "Inequalities Quiz Set 050" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2018-01-02.