The example question is "prove that every integer that is divisible by 10 must be an even integer".
However this can be generalized to prove that every x is Q, where is a statement such as "must be an even integer". So what is the best way to approach this proof? Contradiction, contrapositive, direct?
My thinking was:
Question translates to $\forall A(10k=A\rightarrow A = 2c)$, such that $k\in\mathbb Z,c\in\mathbb Z$ (also can someone tell me if this way of translating the question is correct)
Let B be some number that is divisible by 10. In other words, $B=10K$, where $K\in\mathbb Z$
$B = 2(5K)\\B=2P$
Therefore, B is even because for some B, divisible by 10, B must be even by the definition of even numbers.
Is this form the best way to prove these types of questions? Does this count as a proof by contradiction?
Edit: Or would a proof by induction work best here? In that case how would this question be proven (I have an idea; just need a confirmation)?