Question

if A={3,4,5,6,7} B={1,6,7,8,9} then verify n(AUB)=n(A)+n(B)-n(AintersectionB).

Answer 1

A={3,4,5,6,7}
so n(A) = 5
B={1,6,7,8,9}
so n(B) = 5

AUB = {3,4,5,6,7} U {1,6,7,8,9} = {1, 3, 4, 5, 6, 7, 8, 9}
n(AUB) = 8

AПB =  {3,4,5,6,7} П {1,6,7,8,9} = {6, 7}
n(AПB) = 2

LHS = n(AUB) = 8
RHS = n(A) + n(B) - n(AПB) = 5 + 5 - 2 = 8

LHS = RHS. (proved)

Answer 2

n(A) = {3,4,5,6,7} = 5
n(B) = {1,6,7,8,9} = 5

To verify n(AUB) = n(A) +n(B) - n(A∩B)

LHS

n(AUB) = n(1,3,4,5,6,7,8,9)
= 8
RHS

[n(A) + n(B)] - n( 6,7)]
[5+5 - 2]
=10-2
=8

So both LHS = RHS as they both have 8 number of elements.