Question

for any real number x if 0 < x < 3 then 15-8x x2>0 which facts are assumed and which facts are proven in a proof by contrapositive of the theorem

Answer 1

In a proof by contrapositive, we assume the negation of the conclusion and prove the negation of the hypothesis.

Step-by-step explanation:

The given question is stating that for any real number x, if 0 < x < 3, then the expression 15-8x*x^2>0. The question is asking which facts are assumed and which facts are proven in a proof by contrapositive.

In a proof by contrapositive, we assume the negation of the conclusion and prove the negation of the hypothesis. In this case, the negation of the conclusion is 15-8x*x^2≤0, and the negation of the hypothesis is x≤0 or x≥3. So, in the proof by contrapositive, we assume that if x≤0 or x≥3, then 15-8x*x^2≤0. The fact that is assumed is the negation of the hypothesis, and the fact that is proven is the negation of the conclusion.