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7. A proposition is stated below, and just after that you'll find someone's attempt at proving it directly. After carefully reading through both the proposition and the attempted proof, answer the questions that follow. Proposition. The sum of an even and odd number is always congruent to 1 modulo 4. proof. Let x, y E Z and, without loss of generality, suppose a is odd and that y is even. This means x = 2n +1, for some n E Z y = 2n for some n E Z. The sum of these integers equals xty = (2n+1) + 2n = 2n + 1+2n = 4n +1 showing that their sum has remainder 1 when divided by 4. 0 (a) (2 points) Are you convinced that the Proposition as true? (If so rethink your position, perhaps by considering the integers 4 and 7.) Explain why or why not. (b) (8 points) Now that you do not accept the Proposition as true, there must be an error (or multiple errors) in the proof above. Find and explain the error(s) in the attempted proof