In terms of logic and truth tables why is it that the truth table for exclusive or is as follows:
Consider $P$ and $Q$. Let $P + Q$ denote exclusive or. Then if $P$ and $Q$ are both true or are both false then $P + Q$ is false. If one of them is true and one of them is false then $P + Q$ is true. By exclusive or I mean $P$ or $Q$ but not both. I have been trying to figure out why the truth table is the way it is. For example if $P$ is true and $Q$ is true then no matter what would it be true?