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### Question 1

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

- ω means X = Y
- ® means X ≤ Y
- ∇ means X ≥ Y
- © means X < Y
- § means X > Y

**Statements: **S § T; T ω U; U ω V; V ω W;

**Conclusions: **

- T ω V
- W © T
- U © S

Which of the above conclusions is/are true?

### Question 2

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

- λ means X = Y
- £ means X ≤ Y
- ® means X ≥ Y
- ∀ means X < Y
- ∅ means X > Y

**Statements: **P ∅ Q; Q ∅ R; R ∅ S; S ∀ T;

**Conclusions: **

- T ∀ Q
- R ∀ P
- T ∀ R

Which of the above conclusions is/are true?

### Question 3

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

- ω means X = Y
- $ means X ≤ Y
- ® means X ≥ Y
- µ means X < Y
- ¥ means X > Y

**Statements: **S $ T; T µ U; U ¥ V;

**Conclusions: **

- S ω V
- S µ U

**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 S ≤ T < U > V. Conclusion I translates to S = V. Conclusion II translates to S < U. 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.

- § means X = Y
- ∧ means X ≯ (not more than) Y
- ⊕ means X ≮ (not less than) Y
- © means X < Y
- $ means X > Y

**Statements: **F § G; G $ H; H ⊕ I;

**Conclusions: **

- H § 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 5

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

- ∇ means X = Y
- λ means X ≤ Y
- ® means X ≥ Y
- √ means X < Y
- ¢ means X > Y

**Statements: **S λ T; T ¢ U; U ∇ V;

**Conclusions: **

- T ¢ V
- U √ T

**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 S ≤ T > U = V. Conclusion I translates to T > V. Conclusion II translates to U < T. 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 ≥.

This Blog Post/Article "Inequalities Quiz Set 023" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.