Which result is being proved below, and what procedure is being used to verify the
Chapter 3, Problem 3.67(choose chapter or problem)
Which result is being proved below, and what procedure is being used to verify the result?We begin with the following proof.Proof First, assume that x is even. Then x = 2a, where a Z. Thus3x 2 = 3(2a) 2 = 6a 2 = 2(3a 1).Since 3a 1 is an integer, 3x 2 is even.Next, suppose that x is odd. Then x = 2b + 1 for some integer b. So3x 2 = 3(2b + 1) 2 = 6b + 1 = 2(3a) + 1.Since 3a is an integer, 3x 2 is odd.We can now give the following proof.Proof First, assume that 3x 2 is even. From the preceding result, x is even and so x = 2a,where a Z. Thus5x + 1 = 5(2a) + 1 = 2(5a) + 1.Since 5a is an integer, 5x + 1 is odd.Next, assume that 3x 2 is odd. Again, by the preceding result, x is odd. Hence x = 2b + 1 for someinteger b. Therefore,5x + 1 = 5(2b + 1) + 1 = 10b + 6 = 2(5b + 3).Since 5b + 3 is an integer, 5x + 1 is even.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer