Sets-Relations-And-Functions Question 132

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

Options:

A) 1 only

B) 2 only

C) 3 only

D) 1, 2 and 3

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a]Since, power set is the collection of all the subsets of the set A therefore $ AUP(A)=P(A) $
    $ \therefore $ statement (1) is correct.