1) Suggest the set of all numbers of form a/(2^n) where a is an integer and n is nonnegative integer (that is n is greater than or equal to 0). This is called the set of dyadic rationals. Is this set closed under addition? If so, provide a proof, but if not, provide a counter example.
2) Use a truth table to prove that the compound statement "not(if A, then B)" is equivalent to "A and not B".