inclusion theorem.pptx

Benificial to science students

1. Prof.Jadhav Shailesh S. Dept . of Mathematics Sundarrao More College, Poladpur

2. TOPIC Inclusion – Exclusion Theorem

3. 1) Inclusion exclusion theorom for three properties If N is total number of objects. a1, a2, a3 be the three properties. N(a1)=total number of objects having property a1. N(a2)=total number of objects having property a2. N(a3)=total number of objects having property a3.

4. N(a1,a2)=number of objects having both property property a1 &a2. N(a1,a3)=number of objects having both property property a1 &a3. N(a2,a3)=number of objects having both property property a2 &a3. N(a1,a2,a3)=number of objects having property property a1 ,a2,a3.

5. P(a1)=number of objects not having property a1 P(a2)=number of objects not having property a2 P(a3)=number of objects not having property a3

6. P(a1,a2)=number of objects not having both property property a1 &a2. P(a1,a3)=number of objects not having both property property a1 &a3. P(a2,a3)=number of objects not having both property property a2 &a3. P(a1,a2,a3)=number of objects not having property property a1,a2 & a3.

7. Then, P(a1,a2,a3)=N-N(a1)-N(a2)-N(a3)+N(a1,a2) +N(a1,a3)+N(a2,a3)-N(a1,a2,a3)

8. Example In S.M. College Poladpur,there are 505 stackholders of which 60 stackholder have casualties of their relatives,386 stackholders families remained safe and 68 families have casualties at there neighbours.51 stacke holders lost their family members. 18 lost family members and neighbours , 22 lost both relatives and family members, 30 lost neighbours and relatives. How many stack holders are most suffered?

9. Solution : a2:. a3: N=54,N(a1)=37,N(a2)=25,N(a3)=14,N(a1,a2)=13, N(a1,a3)=9,N(a2,a3)= 7 , N(a1,a2,a3)= x . P(a1,a2,a3)= 2 P(a1,a2,a3)=N-N(a1)-N(a2)-N(a3)+N(a1,a2) +N(a1,a3)+N(a2,a3)-N(a1,a2,a3) 2 =54-37-25-14+13+9+7-x =7-x that is x =5

10. CONCLUSION Most suffered families are 10.

11. VENN DIAGRAMM 10 8 12 20 21 30 18 386

12. Inclusion Exclusion Theorem For Four Property P(a1,a2,a3,a4)=N –N(a1)-N(a2)-N(a3) -N(a4)+N(a1,a2) +N(a1,a3)+N(a1,a4)+N(a2,a3)+N(a2,a4)-N(a1,a2,a3) -N(a1,a2,a4)-N(a2,a3,a4)+N(a1,a2,a3,a4).

13. THANK YOU