Question

Let U = {x / x ∈ N, x < 10}

A = {a / a is even, a ∈ U}

B = {b / b is a factor of 6, b ∈ U}

Verify that n(A) + n(B) = n(A ∪ B) + n(A ∩ B) ​

Answer 1

Step-by-step explanation:

Given, U = {x / x ∈ N, x < 10}

U={1,2,3,4,5,6,7,8,9}

n(U)=9

A = {a / a is even, a ∈ U}

=>A={2,4,6,8}

n(A)=4

B = {b / b is a factor of 6, b ∈ U}

B={1,2,3,6}

n(B)=4

AUB={2,4,6,8}U{1,2,3,6}={1,2,3,4,6,8}

n(AUB)=6

AnB={2,4,6,8}n{1,2,3,6}={2,6}

n(AnB)=2

n(A)+n(B)=4+4=8----(1)

n(AUB/+n(AnB)=6+2=8----(2)

from(1)&(2)

n(A) + n(B) = n(A ∪ B) + n(A ∩ B)