Prove a relation is a equivalence

Question

Let $\sim$ be defined so that $a\sim b$ when $a+b$ is even. Is this an equivalence relation?

Equivalence relations confuse me a lot, so any help is appreciated!

Answer 1

• $a+a=2a$ even so $a\sim a$
• If $a\sim b$ so $a+b=b+a$ is even so $b\sim a$
• If $a\sim b$ and $b\sim c$ then $a+b$ and $b+c$ are even so $a+2b+c$ is even hence $a+c$ is also even: $a\sim c$ so we verified the reflexivity, symmetry and the transitivity. Conclude