How many elements has P (A), if A = Φ?

Solutions:

We know that if A is a set with m elements, then P(A) represents the power set of A which means a set containing all subsets of A.

the number of elements of A is,

n(A) = m and

the number of elements of P(A) is,

n[P(A)] = 2^m

If A = Φ, then n (A) = 0 (as Φ means a null set).

Therefore, the number of elements of P(A) is

n[P(A)] = 2⁰ = 1.

Hence, P(A) has one element.

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.3 Question 5

How many elements has P(A), if A = φ?

Summary:

It is given that A = Φ. We have found that P(A) has one element.Here P(A) represents the power set of A which means a set containing all subsets of A