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### Question 1

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

- « means X = Y
- Γ means X ≯ (not more than) Y
- ⊗ means X ≥ Y
- ∧ means X < Y
- η means X > Y

**Statements: **B ∧ C; C ∧ D; D ⊗ E;

**Conclusions: **

- D η 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 D > 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 2

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

- ∑ means X = Y
- Ω means X ≤ Y
- ® means X ≮ (not less than) Y
- Θ means X < Y
- @ means X > Y

**Statements: **L Ω M; M Θ N; N Θ O;

**Conclusions: **

- L Θ O
- N ∑ 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 L ≤ M < N < O. Conclusion I translates to L < O. Conclusion II translates to N = 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 3

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

- Θ means X = Y
- Ω means X ≯ (not more than) Y
- $ means X ≮ (not less than) Y
- « means X < Y
- η means X > Y

**Statements: **F Θ G; G « H; H η I;

**Conclusions: **

- F Θ I
- H η F

**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 F = G < H > I. Conclusion I translates to F = I. Conclusion II translates to H > F. 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.

- Ω means X = Y
- η means X ≯ (not more than) Y
- ∏ means X ≮ (not less than) Y
- ρ means X < Y
- √ means X > Y

**Statements: **F Ω G; G ρ H; H ∏ I;

**Conclusions: **

- H Ω I
- H √ I

**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 F = G < H ≥ I. Conclusion I translates to H = I. Conclusion II translates to H > I. So we can see that either I or II can be true.

### Question 5

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

- λ means X = Y
- « means X ≤ Y
- ∀ means X ≥ Y
- $ means X < Y
- Ξ means X > Y

**Statements: **T Ξ U; U Ξ V; V λ W;

**Conclusions: **

- T Ξ W
- T Ξ 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: a**

The statements can be translated to T > U > V = W. Conclusion I translates to T > W. Conclusion II translates to T > V. So we can see that both I and II are true.

This Blog Post/Article "Inequalities Quiz Set 026" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-04-07.