Question

Anyone able to assist?

Use mathematical induction to prove that the number of subsets of a set with k elements is given by 2^k, where k = 0,1,2,3...

Answer 1

Base case is the empty set.

Answer 2

Then if a set length \(k\) has \(2^k\) subsets, try to show it must be true that a \(k+1\) length set has \(2^{k+1}\) subsets.

Answer 3

Not sure, I follow. But, thanks.

Answer 4

Okay, suppose a \(k\) element set has \(m\) subsets.

Answer 5

If you add a new element to it, how many more subsets does it have?

Answer 6

K + M?