Sets Relations And Functions Question 33
Question: If $\mathrm{P}(\mathrm{A})$ denotes the power set of A and A is the void set, then what is number of elements in $P(P(P(P(A))))$
Options:
A) 0
B) 1
C) 4
D) 16
Show Answer
Answer:
Correct Answer: D
Solution:
- [d]Since, A is void set therefore the number of elements in power set of A is 1.
$ \therefore P{P(A)}=2^{1}=2 $
because if set A has n elements then $ P(A) $ has $ 2^{n} $ elements.
$ \Rightarrow P{{{P{P(A)}=2}}^{2}}=4 $
$ \Rightarrow P{P{P{P(A)}}}=2^{4}=16 $
BETA
