Consider the following statement. For every integer m, 7m 4 is not divisible by 7. Construct a proof for the statement by select

Question

1 year ago

11

ing sentences from the following scrambled list and putting them in the correct order.

1 answer:

Maksim231197 [3] · Answer 1 · 2023-06-10T00:23:57+03:00

The constructed proof is given below.

<h3>Calculations and Parameters</h3>

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...

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