It is not that 'it just is' it is that you just don't care. and are simply variable place holders for statements. Let's say, for example, that in a particular logical argument, represents the statement, "The color of the sky today is a particularly lovely azure hue." In the course of this argument, you need to repeat that statement 17 times. Would you rather write "The color of the sky today is a particularly lovely azure hue." 17 times or would you rather write 17 times?
Having and stand for statements in general allows us to discuss the rules of logic without reference to specific statements that could possibly cloud the issue. Illustrating the concept of logical conjuction is much easier using AND as opposed to "The sky is blue" AND "The grass is green". I would rather deal with OR as a concept rather than try to understand logical disjunction using "he walked to work" OR "he carried his lunch"
This is very similar to the way we learned to describe general rules when we began our study of Algebra. Everyone knows that 2 + 3 is the same thing as 3 + 2. But without symbols that can stand for any value, it would be difficult to describe the commutative property of addition: .
and function in the same way as shortcut tools for the study of logic and propositional calculus.
John
My calculator said it, I believe it, that settles it
