posted by Christopher on .
In a family six members eat meat; five members eat fish while two eat both. Calculate the number of members in the family.
How do we solve these ones? Hints please...
Draw a Venn diagram. Look for the intersections.
For this problem, let the two circles represent how many people eat meat an d fish, respectively.
In this case, 2 eat both.
So, put a 2 in the place where the two circles intersect.
Now, since we know that 6 eat meat, and we've already determined that 2 eat both, that means that 4 eat only meat. Put a 4 in the meat circle, outside the intersection.
Now, do the same for the fish circle. Place a 3 in the fish-only part of the circle.
Now we see that there are 4+2+3=9 people altogether.
Or, algebraically, if you just add up the meat and fish numbers, you get 6+5=11 people. But note that you've counted the meat&fish people twice, so the actual population is 6+5-2=9
In set notation,
|AUB| = |A| + |B| - |A∩B|