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Prove by contradiction that 17n + 2 is odd --> n is odd.

Prove by contradiction that 17n + 2 is odd --> n is odd.

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Answer #1

Solution:

Given,

=>if 17n + 2 is odd then n is odd

Explanation:

=>Let say p = 17n + 2 is odd and q = n is odd.

=>The given statement is p -> q

Finding contradiction of p -> q:

=>Contradiction of p -> q = ~q -> ~p

=>~q means n is even and ~p means 17n + 2 is even.

Proving ~q -> ~p:

=>As n is even so put n = 2m where m is any positive integer.

=>17n + 2 = 17(2m) + 2

=>17n + 2 = 2(17m + 1)

=>As the result (17m + 1) is multiplied by 2 so whatever value of 17m + 1, it will become even after multiplies by 2.

=>Hence on the basis of above statements we have proved our result.

I have explained each and every part with the help of statements attached to the answer above.

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