There are times in statistics when we have to fight the English language because we need a more specific and precise definition of the English word (bias, plausible, significant). “OR” is a classic example.
Applebees “OR”
You decide to go to Applebees for lunch and order the Triple Bacon Burger®. The server smiles and proceeds to ask you a very important question:
“Would you like french fries OR onion rings?”
In this context, “OR” means one or the other but not both (you would be charged extra to get both).
Starbucks “OR”
After your lunch visit to Applebees, you decide to get a pick-me-up at Starbucks. You order a (too bitter) cup of the house blend. The barista smiles and proceeds to ask you a very important question:
“Would you like cream OR sugar?”
In this context, “OR” means one or the other or both.
So which “OR” do we want for Statistics?
The winner here is Starbucks. When we are thinking about the event A OR B, this includes 3 possibilities: (1) only A, (2) only B, (3) A and B (this would be the left pacman, the right pacman, and the football in a Venn Diagram).
As a final note, logicians and computer scientists make a clear distinction between the inclusive or and the exclusive or.