Asked by Christopher
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...
How do we solve these ones? Hints please...
Answers
Answered by
Steve
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 <b>only</b> 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|
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 <b>only</b> 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|
Answered by
Christopher
Alright!! Thanks!!