Question

For a set A, consider the following statements 

I. A ∪ P(A) = P(A) 

II. {A} ∩ P(A) = A

III. 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

Answer 1

Correct option is (b)

Explanation :

Let A = { 1,2 } and {A} = {1, 2} 

⇒ P(A) = {{ 1 },{ 2 },{ 1, 2}, φ}, 

Then, A ∪ P(A) ≠ P(A) 

and {A} ∩ P(A) = {{1,2} ∩ {1},{2},{1,2}, φ }

= { 1,2 } =  A