Proposition For each real number x x1 x 14 If we multiply b

Proposition. For each real number x, x(1- x) <= 1/4 . Proof. A proof by contradiction will be used. So we assume the proposition is false. This means that there exists a real number x such that x(1 - x) > 1/4 . If we multiply both sides of this inequality by 4, we obtain 4x(1- x) > 1. However, if we let x D 3, we then see that

4x(1- x) > 1

4*3(1 - 3) > 1

-12 > 1

The last inequality is clearly a contradiction and so we have proved the proposition.

Solution

True