Chapter 5.4, Problem 7CYU

To determine

The conclusion of average points per game.

Explanation of Solution

Given information:

Christina scored $13$ points for her high school lacrosse team during the last six games. Prove that her average points per game was less than $3$ .

Calculation:

Given: Let $a$ be Christina’s average given by $a=\frac{\text{number of points}}{\text{number of games}}$

Prove: $a<3$

Following steps are used for the indirect proof are as shown below:

Firstly, make an assumption that the conclusion is false by assuming that the opposite is true. The negation of $a<3$ is $a\ge 3$ . So, assume that $a>3$ or $a=3$ is true.

Secondly, use a logical reasoning or some other fact, such as definition, postulates theorem, or corollary to show that the assumption leads to a contradiction of the hypothesis.

When $a>3$ , $\frac{13}{6}>3\Rightarrow 2.2\cancel{>}3$

When $a=3$ , $\frac{13}{6}=3\Rightarrow 2.2>\cancel{=}3$

In both the steps, the assumption leads to the contradiction of the given information that $a<3.$ Hence, the assumption that $a\ge 3$ must be false, so the Christina’s average points per game less than $3$ .