5.71. Below is given a proof of a result. What result is proved? Proof Let a, b, Ce Z such that a² + b² = c². Assume, to the contrary, that a, b and c are all odd. By (the contrapositive of) Theorem 3.12 O, a? and b? are both odd. Therefore, a? = 2r +1 and b = 2s +1 for integers r and s. Thus, a? + b² = 2r + 2s + 2 = 2 (r + s+1). Since r + s+1 is an integer, a? + b is even. However, a? + b² = c² and c2 is odd. This is a contradiction.

5.71. Below is given a proof of a result. What result is proved? Proof Let a, b, Ce Z such that a² + b² = c². Assume, to the contrary, that a, b and c are all odd. By (the contrapositive of) Theorem 3.12 O, a? and b? are both odd. Therefore, a? = 2r +1 and b = 2s +1 for integers r and s. Thus, a? + b² = 2r + 2s + 2 = 2 (r + s+1). Since r + s+1 is an integer, a? + b is even. However, a? + b² = c² and c2 is odd. This is a contradiction.

Name: what mistakes are found in this proof 5.71. Below is given a proof of
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: what mistakes are found in this proof 5.71. Below is given a proof of a result. What result is proved?Proof Let a, b, Ce Z such that a² + b² = c². Assume, to the contrary, that a, b and c are all odd. By (the contrapositive of) Theorem 3.12 O, a?and