If propositions, then " or " is a proposition (written ); it is true if is true, or if is true (or both).
Note that this is somewhat different from the use of "or" in colloquial English; if both or to be true. This saves us work: we can prove or by just proving ; we don't have to also disprove .
and are true, we still consider
To prove "or ", you can either prove , or you can prove (your choice!)
If you know that "P or Q" is true for some statements P and Q, and you wish to show a third statement R, you can do so by separately considering the cases where P is true and where Q is true. If you are able to prove R in either case, then you know that R is necessarily true.
This technique is often referred to as case analysis.
To disprove " or ", you must both disprove and disprove . Put another way, the logical negation of " or " is "not and not ".