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- Prove that even + odd is odd. 2 answers
I am trying to prove or disprove that if $x$ is even, then $x + 5$ is odd.
This is what I have thus far, but I am stuck:
Assume that the chose variable (x) are in the domain: (x) is an integer
Assume the IF part of the statement: (x) is even
Prove the THEN part: Let a be a dummy variable that we assume is an integer. $x=2a+1$ (Definition of an Odd Integer)
Now find $x+5$.
$x+5=2a+1+5$ (Because we added the same value to both sides of the equation)
$x+5=2(a+3)$ (Because of the Distributive Property of Multiplication over Addition)
$x + 5 = 2z,$ but this is the definition of an even integer; where did I mess up?