Power set

Probability Level 2

Find the number of elements contained in the power set of the set $T = \{0, 1, 2, 3, 4, 5\}$ .

64 63 62 65

3 solutions

Sai Ram
Jul 10, 2015

The number of elements in the power set of a set is equal to $2^n$ , where $n$ stands for the number of $distinct$ elements in the set.

Nihar Mahajan
Dec 31, 2014

number of elements in set A is 6.

So , either we can choose and make sets of 0 or 1 or 2 or 3 or 4 or 5 or 6 elements to make a power set .

so total elements in power set is

6C0 + 6C1 + 6C2 + 6C3 + 6C4 + 6C5 + 6C6 = 2^6 = 64

FOR n elements , number of elements in power set =

nC0 + nC1 + nC2 + nC3 + ........ + nCn-1 + nCn = 2^n

Actually this is a combinatorial problem!

@Nihar Mahajan , You didn't know LaTeX when you typed this XD

Mehul Arora - 5 years, 11 months ago

Yeah , I didn't know Latex at that time. :P

I have figured out how you reached this problem. You stalked my solutions section right? :P :P :P

Nihar Mahajan - 5 years, 11 months ago

Yeah xD xD xD

Mehul Arora - 5 years, 11 months ago

Vishal S
Dec 30, 2014

number of power sets of a set is given by 2^n, where n is number of elements

since the number of elements in the given set is 6

therefore number of power sets in A = {0, 1, 2, 3, 4, 5} is 2^6=64

sorry , but 2^n is the number of sets in the power set , not the number of powersets! thanks.

Nihar Mahajan - 6 years, 5 months ago