### Instruction: There are 42 people in pilates class.  Today, 36 of them brought yoga mats, 26 of them brought eco-friendly water bottles, and 20 of them remembered to bring both yoga mats and water bottles.  How many people had to suffer through class having neither a yoga mat nor a water bottle?### Response: I need to find out how many people out of the 42 had neither a yoga mat nor a water bottle.
I can use a Venn diagram to represent the situation and help me visualize the overlaps.
I'll draw a circle for the yoga mat people and another circle for the water bottle people, and overlap them where they have both.
The region where they overlap is 20, since that's how many people brought both items.
The region where only the yoga mat circle is shaded is 36 - 20 = 16, since that's how many people brought only a yoga mat.
The region where only the water bottle circle is shaded is 26 - 20 = 6, since that's how many people brought only a water bottle.
The region where neither circle is shaded is what I'm looking for, since that's how many people brought neither item.
To find that region, I can subtract the sum of the other regions from the total number of people.
That is, 42 - (20 + 16 + 6) = 0.
So there were no people who had neither a yoga mat nor a water bottle.