Question #5348

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.

Expert's answer

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.

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.

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