Recall some proof techniques: - To prove " Elm . . .", say what m is. - To prove " Va: . . .", begin by xing a generic m. - To prove " P ==> Q", assume P is true and show that Q is true. Write formal, rigorous proofs for these statements: '1. In tutorial '1, we have defined several concepts. Let A be a nonempty subset of R. We say A is excited if 3a E R such that Va E A,::r; 2 a. We say A is happy if 3a. 6 A such that Va: 6 Ass 2 (1.. Below are three claims. Which ones are true and which ones are false? If a claim is true, prove it. If a claim is false, provide a counterexample and a justification of how the counterexample shows the claim is false. (a) If A is happy, then A is excited. (b) If A is excited, then A is happy