1. Hello, can you please help me answer question 3. thank you!

2. The Fibonacci sequence are integers obtained by summing the two preceding num- bers in the sequence. Let F be the set of Fibonacci numbers, typically given by F ={1,1,2,3,5,8,13,21,...}. Prove F is infinite: P: n N,|F| = n.

1. (3 pts) Convert to a formal statement: An integer plus its square is always even. 2. (10 pts) A binary string is any sequence of zeros and ones. Let A be the set of binary strings having twice as many O's as 1's. Prove by contradiction that A is of infinite size. That is, prove by contradiction: P: n E N, IA-n 3. (10 pts) The Fibonacci sequence are integers obtained by summing the two preceding num bers in the sequence. Let F be the set of Fibonacci numbers, typically given by F = 11,1,2,3, 5, 8, 13, 21,... Prove F is infinite: P: neN, FIn. 4. (6 pts) Prove by direct proof (general). P: he Zo, + 1 ZE