Question

Math 210 Weekly Proof #1 Chapter 2 - Proofs Remember that when writing proofs, you will be graded both on the correctness of your logic and on the clarity of your writing. Use complete sentences, and refer to section 2.3 for general writing advice. (4 points) Prove the following proposition: 1. If x and y are perfect squares, then xy is a perfect square. 2. (2 points) Disprove the following proposition: If xy is a perfect square, then x and y must be perfect squares. 3. (4 points) Prove or disprove the proposition: if n is an integer such that n > 3 and 2" – 1 is prime, then n must be odd.

Answer 1

. Solution :- is a perfect square prove - If n and y are perfect square, then ny Troof :- n is a perfect square this means there exist inteqes in such that = m2 y is a perfect square this means there enist wirteges n such that y=k. consider, ny = m . n a lusing law of enponents) As product of two integens is an integer therefore, mn is an integer. As there must an integer man whose square is is a perfect square. us 2 iony us a Scanned with CamScanner