Question

if i know an even plus even equals and even number. then can i suppose for contradiction that an even plus and even equals and odd, and give an example like 2+2 is even thus concluding that and even plus even must be even?

Answer 1

you can prove it directly

any even number is of the form 2*k where k is an integer

so let

x = 2*m
y = 2*n

m,n are integers so that means x and y are even numbers

Answer 2

add them up

x+y = 2*m + 2*n = 2*(m+n) = 2*p

where p = m+n is an integer (summing two integers yields another integer)

so because x+y = 2*p this means x+y is even too

Answer 3

yes, thank you but is the contradiction statement true, i believe it is not but dont know why

Answer 4

you could do a proof by contradiction, but it would follow basically the same steps as shown above

step 1) assume `even` plus `even` is `odd`

step 2) go through the work shown above

step 3) step 2 will conclude with x+y being even, which contradicts the assumption in step 1

Answer 5

okay thank you

Answer 6

no problem