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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
- Γ means X ≥ Y
- ⊕ means X < Y
- ∑ means X > Y

**Statements: **G ∑ H; H ⊕ I; I ⊕ J;

**Conclusions: **

- H ⊕ J
- H Γ J

**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 G > H < I < J. Conclusion I translates to H < J. Conclusion II translates to H ≥ J. 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 2

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

- ω means X = Y
- Δ means X ≤ Y
- @ means X ≮ (not less than) Y
- ∅ means X < Y
- Ω means X > Y

**Statements: **K Ω L; L Ω M; M @ N;

**Conclusions: **

- M Ω N
- M ω 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: d**

The statements can be translated to K > L > M ≥ N. Conclusion I translates to M > N. Conclusion II translates to M = N. 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 3

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

- ⊕ means X = Y
- ω means X ≯ (not more than) Y
- Δ means X ≥ Y
- µ means X < Y
- « means X > Y

**Statements: **M « N; N µ O; O Δ P;

**Conclusions: **

- O « P
- O ⊕ 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: d**

The statements can be translated to M > N < O ≥ P. Conclusion I translates to O > P. Conclusion II translates to O = P. 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 4

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

- µ means X = Y
- ∧ means X ≤ Y
- ∀ means X ≮ (not less than) Y
- Ξ means X < Y
- § means X > Y

**Statements: **N ∀ O; O § P; P § Q;

**Conclusions: **

- N µ Q
- 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 N ≥ O > P > Q. Conclusion I translates to N = Q. Conclusion II translates to N > P. So we can see that only conclusion II is true.

### Question 5

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

- ≅ means X = Y
- Γ means X ≤ Y
- η means X ≥ Y
- ∇ means X < Y
- µ means X > Y

**Statements: **T µ U; U µ V; V Γ W;

**Conclusions: **

- T ∇ W
- V µ T

**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 T > U > V ≤ W. Conclusion I translates to T < W. Conclusion II translates to V > T. So we can see that neither I nor II is true.

This Blog Post/Article "Inequalities Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-05-17.