The constructed proof is given below.
Calculations and Parameters
Prove: f(M)= 7M +4 is not divisible by 7 for any integer M.
M=0 --> f(M) = 4 which is not divisible by 7.
M=1 --> f(M) = 11 which is not divisible by 7.
Suppose f(M) is not divisible by 7 for some positive integer M.
(this is the GIVEN induction hypothesis)
7(m+1)+4 = 7m+7+4 = 7m +4 + 7 = (7m+4)+7
dividing by 7, the quotient is [(7m+4)+7]/7
= (7m+4)/7 + 1
This is NOT divisible by 7 per induction hypothesis...
Read more about discrete mathematics here:
https://brainly.com/question/27793609
#SPJ1
