Question

some venn diagrams have more than two circles in them, like this example. 1) how many students like swimming or baseball but not badminton ? _ 2) how many students like both baseball and badminton ? _ 3) how many students only like baseball ? _ 4) how many students like swimming or baseball ? _ 5) how many students like baseball or badminton ? _ 6) how many students do not like either swimming or badminton ? _ 7) how many students like both swimming and baseball ? _ 8) how many students do not like either swimming or baseball ? _ 9) how many students do not like both swimming and baseball ? _ 10) how many students do not like both baseball and badminton ? _

Explanation:

Step1: Find students who like Swimming or Baseball but not Badminton

Add the number of students who like only Swimming (18), only Baseball (20) and those who like Swimming and Baseball but not Badminton (2). So, $18 + 20+2=40$.

Step2: Find students who like both Baseball and Badminton

Add the number of students in the intersection of Baseball and Badminton circles, which is $6 + 3=9$.

Step3: Find students who only like Baseball

The number of students who only like Baseball is 20.

Step4: Find students who like Swimming or Baseball

Use the principle of inclusion - exclusion. $(18 + 2+6 + 20)=46$.

Step5: Find students who like Baseball or Badminton

$(20+2 + 6+3+10 + 21)=62$.

Step6: Find students who do not like either Swimming or Badminton

The number of students outside the Swimming and Badminton circles is 13.

Step7: Find students who like both Swimming and Baseball

The number of students in the intersection of Swimming and Baseball circles is $2+6 = 8$.

Step8: Find students who do not like either Swimming or Baseball

The number of students outside the Swimming and Baseball circles is $13+21 = 34$.

Step9: Find students who do not like both Swimming and Baseball

Add all the numbers outside the intersection of Swimming and Baseball circles: $13+21 + 10+3=47$.

Step10: Find students who do not like both Baseball and Badminton

Add all the numbers outside the intersection of Baseball and Badminton circles: $13+18+20 = 51$.

Answer:

1. 40
2. 9
3. 20
4. 46
5. 62
6. 13
7. 8
8. 34
9. 47
10. 51