There is the case of a vacuously true statement. For example let's use the set { 1,2,3,4,5} Let A be the statement this set contains all the numbers that are both even and odd. Since there aren't numbers that are both even and odd then both A and ~A are true.
I am really sorry but can u plz answer how to translate "since"to a symbol? Wud it just be an arrow? "Since the safe was opened, it must have been blah