Answer to Question #5348 in Discrete Mathematics for Leonette Roberts

Question

Define a set X recursively as follows:
B. 4 is a member of X
R. if x is a member of X then 3x + 24 is a member of X
Use mathematical induction to prove that every element of X is even.

Answer 1

Basis:
1. The first member of a set is 4 and it is even. The second member of a set is 3*4+24 = 36 and it is even too.
Step of induction:
2. Let x be the even element of X. So, exists some natural n that x=2n and 3x + 24 = 3*2n + 24 = 2(3n + 12) is even too.