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|
Alright!! Thanks!!
To solve this problem, we can use a method called "Inclusion-Exclusion Principle." Here's how you can apply it:
1. Start by adding the number of family members who eat meat (6) and the number of family members who eat fish (5). This gives us a total of 11 members so far.
2. However, we have double-counted the two members who eat both meat and fish. To correct this, we subtract the number of members who eat both from the total.
3. The final step is to subtract the number of members who eat both (2) from the total (11). This gives us the number of unique family members.
So, the number of members in the family is 11 - 2 = 9. There are 9 members in the family.
To solve this problem, we can use a concept called the Principle of Inclusion-Exclusion. Here's how you can approach it:
1. Let's assume there are a total of x members in the family.
2. Out of the six members who eat meat, two members also eat fish. So, the number of members who only eat meat is 6 - 2 = 4.
3. Out of the five members who eat fish, two members also eat meat. So, the number of members who only eat fish is 5 - 2 = 3.
4. To find the total number of members in the family, we need to count both the members who exclusively eat meat and those who exclusively eat fish, as well as the members who eat both.
5. We can use the Principle of Inclusion-Exclusion to calculate the total number of members:
Total number of members = (members who eat meat) + (members who eat fish) - (members who eat both)
Total number of members = 4 + 3 - 2
Total number of members = 5
So, there are 5 members in the family.