Question: Select the mistake that is made in the proof given below. Theorem. The sum of two odd integers is even. Proof. Since x is
Select the mistake that is made in the proof given below. Theorem. The sum of two odd integers is even. Proof. Since x is odd, x = 2k + 1 for some integer k. Since y is odd, y = 2j + 1, for some integer j. Plugging in the expression 2k + 1 for x and 2j + 1 for y into x + y gives x + y = (2k + 1) + (2j + 1) = 2k +2k + 2 = 2(k+j+1) Since k and j are integers, k+j+1 is also an integer. Therefore, since x + y is equal to 2m, where m=k+j+1 is an integer, x + y is even. a. Generalizing from examples. b. Misuse of existential instantiation. c. Failure to properly introduce a variable. d. Assuming facts that have not yet been proven.
Step by Step Solution
3.41 Rating (157 Votes )
There are 3 Steps involved in it
The detailed answer for the above question is provided belo... View full answer
Get step-by-step solutions from verified subject matter experts
