For a set A, consider the following statements
1. A ∪ P(A) = P(A)
2. {A} ∩ P(A)=A
3. P(A) - {A} = P{A}
where P denotes power set.
Which of the statements given above is/are correct?
a)
I only
b)
II only
c)
III only
d)
I, II and III
Correct answer is option 'B'. Can you explain this answer?

Question

For a set A, consider the following statements
1. A ∪ P(A) = P(A)
2. {A} ∩ P(A)=A
3. P(A) - {A} = P{A}
where P denotes power set.
Which of the statements given above is/are correct?

a)
I only
b)
II only
c)
III only
d)
I, II and III

Correct answer is option 'B'. Can you explain this answer?

Answer

Let A = {1,2} and {A} = {(1,2)} implies,P(A) = {{1}, {2},.{1,2}, φ}
Then, A ∪ P(A) ≠ P(A)
and{A} ∩ P(A) = {{ l , 2}} ∩ {{1}, {2}, {1,2},φ}
= {1,2}=A

Answer

Is a collection of elements.
2. The elements in A are distinct.
3. A has a specific order.
4. A can be finite or infinite in size.
5. A can be empty.
6. The elements in A can be of any type.

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