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### Question 1

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.

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.

- Δ means X = Y
- @ means X ≯ (not more than) Y
- ⊗ means X ≥ Y
- ® means X < Y
- ∧ means X > Y

**Statements: **B ® C; C ® D; D Δ E;

**Conclusions: **

- B ® D
- D ∧ B

**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 > B. 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.

- ∃ means X = Y
- ∩ means X ≤ Y
- ⊕ means X ≥ Y
- £ means X < Y
- ρ means X > Y

**Statements: **S ∩ T; T £ U; U ⊕ V;

**Conclusions: **

- S ρ V
- S £ 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 S < V. So we can see that either I or II can be true.

### Question 4

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

- % means X = Y
- @ means X ≯ (not more than) Y
- ¥ means X ≮ (not less than) Y
- ρ means X < Y
- η means X > Y

**Statements: **J ¥ K; K % L; L ρ M;

**Conclusions: **

- J η L
- K ¥ 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: c**

The statements can be translated to J ≥ K = L < M. Conclusion I translates to J > L. Conclusion II translates to K ≥ M. So we can see that only conclusion I is true.

### Question 5

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

- ρ means X = Y
- η means X ≤ Y
- Γ means X ≮ (not less than) Y
- « means X < Y
- Ω means X > Y

**Statements: **N Γ O; O Ω P; P η Q;

**Conclusions: **

- O Ω Q
- N Ω Q

**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 N ≥ O > P ≤ Q. Conclusion I translates to O > Q. Conclusion II translates to N > Q. So we can see that neither I nor II is true.

This Blog Post/Article "Inequalities Quiz Set 035" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.