contestada

Using the definitions of even integer and odd integer, give a proof by contraposition that this statement is true for all integers n : If 3 n - 5 is even, then n is odd.

Respuesta :

LammettHash
Suppose [tex]n[/tex] is even, i.e. there is some integer [tex]k[/tex] such that [tex]n=2k[/tex]. Then

[tex]3n-5=3(2k)-5=6k-5=6k-6+1=2(3k-3)+1=2K+1[/tex]

where [tex]K[/tex] is just some other integer. Therefore [tex]3n-5[/tex] is odd, proving the contrapositive, and so the original statement is also true.

Otras preguntas