Suppose s is a recursively defined set, defined by - the number 1 is in s - if n is in s, then so is 3n + 2 - if n is in s, then so is 5n - 1 - if n is in s, then so is n + 7. suppose you want to prove using structural induction that all members of s have a certain property. what do you have to prove in the base step?

See answer below

Step-by-step explanation:

Using structural induction, we would have to prove that 1 and all the numbers derived from this fact, have the property.

That is to say, we would have to prove that

1, 3*1+2, 5*1-1 and 1+7 = {1, 4, 5, 8} have the property we want to prove S has.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: