Consider the indirect proof and form your proof based on it.
See solution.
Practice makes perfect
We have been given a paragraph proof. We will examine the given information and the statement that we will prove to fill in the blanks.
Given: &The total membership of the Yoga
&Club and the Go Green Club is fewer
&than $20.$
&The Go Green Club has $10$ members.
Prove: &The Yoga Club has
&fewer than $10$ members.
We will complete the proof writing an indirect proof. Thus, the proof starts with assuming temporarily that the Yoga Club has 10 or more members. According to the assumption, let's start to fill in the blanks.
Blank a.
Based on the given information that The Go Green Club has 10 members and the assumption, we can immediately say that the two clubs have 20 or more members.
Statement
This means that together the two clubs have
a. $20$ or more members.
Blank b.
In this part, we need to have a contradiction. Since the total membership of the two clubs is fewer than 20 is given, we have a contradiction with the previous statement.
Statement
This contradicts the given information that
b. the total membership of the two clubs
is fewer than $20.$
Blank c.
As a result, we proved the given statement by having a contradiction.
Statement
Therefore, it is true that
c. the Yoga Club has fewer than $10$ members.
