# Inequalities Quiz Set 009

### Question 1

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

1. ∧ means X = Y
2. « means X ≤ Y
3. ¥ means X ≥ Y
4. £ means X < Y
5. § means X > Y

Statements: R £ S; S ∧ T; T ∧ U; U ∧ V;

Conclusions:

1. R £ V
2. R § T
3. S ∧ V

Which of the above conclusions is/are true?

A

both I and III.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to R < S = T = U = V.

The conclusions translate to:

1. R < V(True)
2. R > T(False)
3. S = V(True)

### Question 2

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

1. © means X = Y
2. ∃ means X ≯ (not more than) Y
3. Ξ means X ≮ (not less than) Y
4. ρ means X < Y
5. Θ means X > Y

Statements: Q Θ R; R © S; S ∃ T;

Conclusions:

1. Q ρ T
2. S Θ 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 Q > R = S ≤ T. Conclusion I translates to Q < T. Conclusion II translates to S > Q. So we can see that neither I nor II 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.

1. Δ means X = Y
2. ® means X ≤ Y
3. © means X ≮ (not less than) Y
4. ∂ means X < Y
5. « means X > Y

Statements: B Δ C; C Δ D; D « E;

Conclusions:

1. B Δ E
2. C « 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: b

The statements can be translated to B = C = D > E. Conclusion I translates to B = E. Conclusion II translates to C > E. 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.

1. λ means X = Y
2. ∩ means X ≤ Y
3. % means X ≥ Y
4. \$ means X < Y
5. Ξ means X > Y

Statements: B λ C; C \$ D; D \$ E;

Conclusions:

1. B \$ D
2. C Ξ 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: c

The statements can be translated to B = C < D < E. Conclusion I translates to B < D. Conclusion II translates to C > E. 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 5

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

1. Γ means X = Y
2. ∧ means X ≤ Y
3. λ means X ≥ Y
4. § means X < Y
5. ∃ means X > Y

Statements: D § E; E Γ F; F § G; G § H;

Conclusions:

1. E § G
2. D § H
3. F § D

Which of the above conclusions is/are true?

A

both I and II.

B

I only.

C

II only.

D

III only.

Soln.
Ans: a

The statements can be translated to D < E = F < G < H.

The conclusions translate to:

1. E < G(True)
2. D < H(True)
3. F < D(False)