Question

If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, then find A intersection B​

Answer 1

Answer:

In A, last term will be 400.

In B, the terms are also in A.P having a common difference of 3.

Hence

a

n

=a

1

+(n−1)d.

Now n=250 for the last term.

Hence

a

250

=3+(250−1).3

=3(1+250−1)

=750.

Now A∩B will have elements which are multiples of 6.

Last term will be 400−4=396.

Hence

a

n

=a+(n−1).d

d=6,n=?,a=6 and a

n

=396

Hence

396=6+(n−1).6

Or

66=n.

Hence

n(A∩B)=66.

Now

n(A∪B)=n(A)+n(B)−n(A∩B)

=200+250−66

=384.