# Inequalities Quiz Set 029

### Question 1

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

1. ∏ means X = Y
2. λ means X ≤ Y
3. ∂ means X ≥ Y
4. Γ means X < Y
5. ≅ means X > Y

Statements: R Γ S; S Γ T; T ∏ U; U ∏ V;

Conclusions:

1. T ≅ V
2. R Γ U
3. R Γ V

Which of the above conclusions is/are true?

A

both II 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. T > V(False)
2. R < U(True)
3. R < V(True)

### Question 2

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: J © K; K ∃ L; L ∇ M;

Conclusions:

1. J % M
2. K % M
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 J < K = L ≤ M. Conclusion I translates to J > M. Conclusion II translates to K > M. 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. ∃ means X = Y
2. ∩ means X ≤ Y
3. Ω means X ≮ (not less than) Y
4. ∇ means X < Y
5. ρ means X > Y

Statements: Q Ω R; R ∇ S; S ρ T;

Conclusions:

1. S ∃ T
2. S ρ 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: b

The statements can be translated to Q ≥ R < S > T. Conclusion I translates to S = T. Conclusion II translates to S > T. 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. ∂ means X = Y
2. ∅ means X ≤ Y
3. § means X ≮ (not less than) Y
4. ¥ means X < Y
5. Ω means X > Y

Statements: S ∂ T; T ∂ U; U § V;

Conclusions:

1. S ∂ V
2. T Ω 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 T > V. 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.

1. @ means X = Y
2. ρ means X ≯ (not more than) Y
3. ¥ means X ≥ Y
4. ∑ means X < Y
5. ω means X > Y

Statements: M ω N; N ∑ O; O ρ P;

Conclusions:

1. M ∑ P
2. N ω P
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 M > N < O ≤ P. Conclusion I translates to M < P. Conclusion II translates to N > P. 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 ≥.