Question

- For the following statement, write down the hypothesis and the conclusion, and then either prove the proposition, or find a counter-example to disprove it. If you prove the proposition, state which proof method you are using. "Every integer greater than 0 can be written in the form 2k.m where k, m EN and m is odd

Answer 1

Answer: Counter-example is 1. There is no k or m ∈ Ν, m odd that makes the statement true for 1.

Explanation:

integer = x

x > 0 ⇒ x = 2k.m k,m∈N and m odd

If x is 1, either k must be 1/2 or m must be 1/2, but they cannot be because the statement says k, m ∈ N. They must be natural.

This way, the statement is not true for every integer greater then 0.