Question

Suni asked 24 people if they liked to roller blad or ice skate. 12 liked to roller blade and 18 liked to ice skate. 3 did not like either. How many liked both?

Answer 1

When you have two overlapping sets, and you count the number of objects in each set, you end up counting the bit in the intersection of the two sets twice, so we have to take that bit away. The algebra looks like this,\[N(A \cup B)=N(A)+N(B)-N(A.and. B)\]

Now, before using this, you know that 3 people like neither, so the total number of people to consider becomes 24-3 = 21.

If your set A is the roller blade set, and B is the ice skate set, you have\[21=12+18-N(A.and.b) \rightarrow N(A.and.B)=30-20=10\]

So 10 people like both.

I don't know what level you're studying at, so hope this is understandable. If you draw a picture of two overlapping circles to represent your sets, the overlap is the set of all people who like both. If you count the number of people in the first set, and then count the number in the second set, you should see that you're counting the number in the intersection (i.e. the people who like both) twice. That's how the formula above is developed.

Answer 2

thanks!

Answer 3

you're welcome :)