Question

Determine whether each of these sets is the power set of aset,wherea and b are distinct elements. a) ∅ c) {∅,{a},{∅,a}} b) {∅,{a}} d) {∅,{a},{b},{a,b}}

Answer 1

Answer:

{∅, {a}, {b}, {a,b}}

Step-by-step explanation:

The value of power of a set is generalized by using the formula,

Power of a set (P) = 2^n where n is the number of element in the set.

Given two distinct elements a and b say;

A = {a,b}

n(A) = 2 i.e the number of elements in the set is 2. Therefore the power of the set will be 2^n which gives 2^2 = 4.

P(A) = 4 means there are 4 subsets of the given set. Subsets are sets of elements that can be found in the set. The subsets of element A will be;

{∅, {a}, {b}, {a,b}} which gives 4 elements in total.

Note that empty set ∅ is always part of the subset of any given set