Construct a proof for 2 of the following. Clearly indicate which two of the three statements you are giving proofs for. • Let n be a positive integer. Prove that if n has a remainder of 2 when divided by 3, then n is not a perfect square. Hint. It is probably easiest to prove the contrapositive of this statement. What are the possible remainders when you divide by n? • Let A and B be sets. Prove that − = − if and only if = . Hint: Since this an "if and only if" statement, you will need to prove both directions. • Let n be a positive integer. Prove that 1 × 1! + 2 × 2! + 3 × 3! + ⋯ + × ! = ( + 1)! − 1.
