Question

Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Determine the truth of the following statement. If the statement is false, give a counterexample. The product of two even numbers is even.

A. false; 8×4=32

B. false; 7 ×6=42

C. false; 3 ×10=30

D. true

Answer 1

Let the two even numbers be
`2p` and
`2q`, where
`p,q \in \mathbb{Z}`.

Then, their product is
`4pq=2(2pq)`. Since
`2pq`, this shows their product is also even.

Therefore, the correct answer is D.