Assume that Toshiro did both activities for less than an hour.
See solution.
Practice makes perfect
We will start with writing the conditional statement we are asked to prove and highlight the hypothesis and the conclusion.
If Toshiro was at the gym for just over
2hoursand did two activities,
then he did one of these activities
for more than1 hour.
To do this we can use an indirect proof.
Step 1
Let's assume that Toshiro did each of these activities for not more than 1 hour. Using S for the total time he spent on swimming, and W for the total time he spent on lifting weighs, we can write this assumption as inequalities.
Assumption: S≤ 1 and W≤ 1
Step 2
Now we will see what this assumption implies for the total time Toshiro spent at the gym, T.
T=S+W≤ 1+1
⇓
T≤ 2
We got that T≤ 2, and this contradicts the hypothesis that Toshiro was at the gym for just over 2 hours.
Step 3
Our assumption led to a contradiction, so the assumption cannot be true.
If Toshiro was at the gym for just over 2 hours and did two activities, then he did one of these for more than an hour.
