Answer to Question #127638 in Discrete Mathematics for Saravanan

Question

In a physics class 40 children had forgotten to bring their physics book,34 had forgotten to do their homework. The teacher asked to borrow the physics book from some one at once. 48 childrens left the room. Draw a Venn diagram and find how many children had forgotten both?

Answer 1

Let A be the event "children had forgotten to bring their physics book", B be the event "children had forgotten to do their homework".

Given $N(A)=40,N(B)=34, N(A\cup B)=48$

Then

$$N(A\cup B)=N(A)+N(B)-N(A\cap B)$$

$$N(A\cap B)=N(A)+N(B)-N(A\cup B)$$

$$N(A\cap B)=40+34-48=26$$

26 children had forgotten both.