Use mathematical induction to prove that for every integer n > =2, if a set s has n elements, then the number of subsets of s with an even number of elements equals the number of subsets of s with an odd number of elements.

1. what expression would be the same as 6x+x+0 2. find the prime factorization of 60 3. write the expression for 6 + x in words.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

The cost for an uberi is $2.50 plus $2.00 mile. if the total for the uber ride was $32.50, how many miles did the customer travel?