 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/2/b/i/solution

n

is both an even number and an odd number. Then

n = 2 u

and

n = 2 v + 1

for some integers

u, v

. Subtracting yields

u - v = 1/2

. The left side is an integer, while

1/2

is not. This contradiction proves that no integer is both even and odd.

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