Question

if A and B are finite sets, then prove that n(A U B) = n(A) + n(B) - n(A ∩ B)​

Answer 1

Answer:

given series is in arithmetic progression

with a=-12 and d=3

sum of n terms of an AP=n/2(2a+(n-1)d)

=>54=n/2(2(-12)+(n-1)3)

=>54=n/2(-24+3n-3)

=>108=n(3n-27)

dividing with 3 on boths sides, we get

=>36=n²-9n

=>n²-9n-36=0

=>n²-12n+3n-36=0

=>n(n-12)+3(n-12)=0

=>(n+3)(n-12)=0

n=12

I hope this will help u :