For the theorem that the product of two even numbers is even, the proof by contradiction assumes the opposite: that the product of two even numbers is odd. The speaker justifies this by stating that if a number is not even, it must be odd.
Conditions: The theorem to be proved is: the product of two even numbers is also even.; The method is proof by contradiction.; The parity dichotomy (not even implies odd) is used as an assumed fact.
For the theorem that the product of two even numbers is even, the proof by contradiction assumes the opposite: that the product of two even numbers is odd. The speaker justifies this by stating that if a number is not even, it must be odd.
Conditions: The theorem to be proved is: the product of two even numbers is also even.; The method is proof by contradiction.; The parity dichotomy (not even implies odd) is used as an assumed fact.