Disjunction: Why did the inclusive "OR" become the convention? In How to Prove it by Velleman, for defining disjunctions, he gives the difference between exclusive "OR", and inclusive "OR." 
Given two events $P$ and $Q$, the disjunction is defined for them as:


*

*Inclusive: One of $P$ and $Q$, or both.

*Exclusive: One of $P$ and $Q$, but not both.
Quoting from his book:
"In mathematics, or always means inclusive or, unless specified otherwise, ..." (Velleman, 2006, p.15)
My question is -

Why did the inclusive definition of disjunction become the convention?

Was it coincidental, or is there some aspect to the inclusive definition that makes it more convenient?

George Boole, when he originally developed his Laws of Thought to apply mathematics to reasoning, used the exclusive or. However, the system was quite cumbersome in comparison to modern methods.
As others took up his ideas, they found that the inclusive or was far better behaved and easier to work with. 
For instance, suppose we want to say "It is not the case that P or Q but not both". We get a "Either it is not the case that P and not the case that Q, or it is the case that both P and Q". 
Contrast this with "It is not the case that P or Q or both". To negate this, we have "It is not the case that P and it is not the case that Q". 
