Question

if n(A)=80 ,n(B)=30,n(AUB)=100 then n{(A-B)U(B-A)}=​

Answer 1

Answer:

if n(A)=80,n(B)=30,n(A U B)=100 then find n [(A-B) U (B-A)]

(: see the first picture in above attachment)

n(A) = x+y

n(B) = y+z

n(A-B) = (x+y)-y = x,

n(B-A) = (y+z)-y = z,

n[(A-B) U (B-A)] = x+z since (A-B) and (B-A) are disjoint

n(A) = x+y = 80

n(B) = y+z = 30

n(A U B) = x+y+z = 100

So we have the system of three equations in three unknowns:

x + y = 80

y + z = 30

x + y + z = 100

Subtracting the first equation from the third gives z = 20

Substituting that in the second equation gives y = 10

Substituting that in the first equation gives x = 70

Now our Venn diagram becomes

(: see the second picture in attachment)

n[(A-B) U (B-A)] = x+z = 70+20 = 90

Edwin

Step-by-step explanation:

I hope it's help you!

.BB