Question

The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is

Answer 1

Answer:

Step-by-step explanation:

There’s a result in mathematics used for this. It says that a power set B of any set A is a set of all the subsets of A and the number of elements of B will be 2^n where n is the number of elements of A.

So taking your question as an example;

A = {1,2,3}

B : set of all subsets of A

List out all the subsets of A - {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}

Number of elements in A (n) = 3 so 2^3 = 8

So, B = {{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}} and the number of elements are 8.

We have defined a set as a collection of its elements so, if S is a set then the collection or family of all subsets of S is called the power set of S and it is denoted by P(S).

Thus, if S = a, b then the power set of S is given by P(S) = {{a}, {b}, {a, b}, ∅}

We have defined a set as a collection of its elements if the element be sets themselves, then we have a family of set or set of sets.

Thus, A = {{1}, {1, 2, 3}, {2}, {1, 2}} is a family of sets.

The null set or empty set having no element of its own is an element of the power set; since, it is a subset of all sets. The set being a subset of itself is also as an element of the power set.

Answer 2

Answer:

8

Step-by-step explanation:

No: of elements in the set is 3   -   (2,3),1 and null set

so the no: of elements in the power set is 2^n

n=3

so 2³=8