1. Hello, can you please help me answer question 2. thank you!

2. A binary string is any sequence of zeros and ones. Let A be the set of binary strings having twice as many 0s as 1s. Prove by contradiction that A is of infinite size. That is, prove by contradiction: P: n N, |A| = n.

CS 222 Homework 4 Write your name on this sheet, and turn it in as a cover sheet with your completed homework. You may turn this assignment in during class or place in the instructor's mailbox up until 5 pm of the due date. Do not place under the door of the instructor's office. Write only on one side of each sheet of paper. Solutions written on the backs of sheet will not be graded. Write clearly, show all work, and write formulas and assumptions used to solve a problenm Do not staple, dog ear, or otherwise attach your papers together. Rubric: 1: 2 points correct use of terms, 2 pts overall correct. 2 and 3: 2 points format, 6 points correct logic for contradiction proof, 2 points conclusion 4: 1 point format, 4 points correct logic for direct proof, 1 point conclusion. 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 0's as 1's. Prove by contradiction that A is of infinite size. That is, prove by contradiction: P: NJA-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 = (1, 1, 2, 3, 5, 8, 13, 21, . . .). Prove F is infinite: P: ,n E N. F-n. 4. (6 pts) Prove by direct proof (general). P: yn E Zo, n. 1 E ZE