suppose that in a bushel of 100 apples there are 20 that hav

suppose that in a bushel of 100 apples, there are 20 that have worms and 15 that have bruises. only apples with neitehr bruises nor worms can be sold. if there are 10 bruised apples tha thave worms in them, how many of the 100 apples can be sold.

Solution

here We are looking for the number of apples that have neither of the having worms or having bruises.

Let P1 denote the property of having worms in apples and P2 denote the property of having bruises.

so,

N(P1) = 20,

N(P2) = 15,

and N(P1P2) = 10

By using the alternative form of inclusion-exclusion, our equation is

N(P\'₁P\'₂) = N N(P1) N(P2) + N(P1P2)

N(P\'₁P\'₂) = 100 20 15 + 10

N(P\'₁P\'₂) = 75

so we can sell 75 of the 100 apples