Prove that if a & b are odd then a+b is even

[sonadoramante]

Summary:: Prove that if a is an odd integer and b is an odd integer then a+b is even.

Theorem: If a is odd and b is odd then a+b is even.

Proof: Let a and b be positive odd integers of the form a = 2n+1 & b = 2m+1

a+b = 2n+1+2m+1
= 2n+2m+1+1
= 2n+2m+2
= 2(n+m)+2
= Let k = n+m
= 2k+2
Therefore a+b is even.

 

[Office_Shredder]

This mostly looks fine, though you might be expected to justify why 2k+2 is even.

 

[pasmith]

Summary:: Prove that if a is an odd integer and b is an odd integer then a+b is even.

Theorem: If a is odd and b is odd then a+b is even.

Proof: Let a and b be positive odd integers of the form a = 2n+1 & b = 2m+1

a+b = 2n+1+2m+1
= 2n+2m+1+1
= 2n+2m+2
= 2(n+m)+2

Why not $2n + 2m + 2 = 2(n + m + 1)$?

= Let k = n+m
= 2k+2
Therefore a+b is even.

 

[sonadoramante]

Aha! That makes more sense.
a+b = 2n+1+2m+1
= 2n+2m+2
= 2(n+m+1)
= 2k
Hence a+b is even. :)

 

[Mark44]

a+b = 2n+1+2m+1
= 2n+2m+1+1
= 2n+2m+2
= 2(n+m)+2
= Let k = n+m
= 2k+2
Therefore a+b is even.

The line "= Let k = n + m" shouldn't be there. The version in post #4 is what you want to say.