Nick Collins, Researcher at University of Chicago, Numerade Educator

01:28

Calculus 3

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 + 2j + 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.