Question

If a set A has four elements then the order of the power set of A is (a) 4 (c) 2 (b) 16 (d) O None of these
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

For a set with n items, the number of elements in its power set is the total number of possible subsets of that set. So how many subsets are there?

Consider this. The A= {x1,x2,..xn} be your set of n elenents. While constructing a subset S, for each element we are faced with a choice: do we include it or not. Since there are n elenents, we get n choices each with 2 possible outcomes. Thus the total number of ways to do it will be 2n .

Thus for 4 elements the number of subsets are 24=16.