Question

A and b are two sets and u is the universal set.If n(u) =100,n(a)=40,n(b)=20 and n(aub) '=50 find n(aub) n(anb) and (a-b)

Answer 1

Answer:

Step-by-step explanation:

n(AUB) = n(U) - n( (AUB)' )

              = 100 - 50

               = 50.

n(A n B)  = n(A) + n(B) - n(AUB)  

                = 40 + 20 - 50

                  = 10.

n(A - B) = n(A) - n(A n B)

               = 40 - 10

               = 30.

Answer 2

Given that,

n(u) =100,n(a)=40,n(b)=20 and n(aub) '=50

That is,

n(aub) = n(u) - n(aub)’

n(aub) = 100 - 50 = 50

Now,

n(aub) = n(a) + n(b) - n(anb)

Therefore,

n(anb) = n(a) + n(b) - n(aub)

= 40 + 20 - 50 = 10

Now

a-b = a - (anb) =40-10 =30