Mathematics

Problem

Consider the claim: "For every integer

n

, the number

n^{2}-2n

is always odd." a. (i) Define the term "counterexample" in the context of mathematical reasoning. b. (ii) Calculate the values of

n^{2}-2n

for

n=0,1,2,3,4

and note whether each result is odd or even. c. (iii) From your calculations in part (ii), identify one value of

n

that shows the given claim is false. Explain clearly why this value of

n

contradicts the claim and, hence, serves as a counterexample.