Question

verify the sule: n (AuB) +n (AnB) = n(A) + n (B) for A={1,2,3,5,7, 9, 11, 13) and B={1,2,4,6,8,12,13)​

Answer 1

Answer:

Step-by-step explanation:

Given,

A = {1,2,3,5,7,9,11,13} and B= {1,2,4,6,8,12,13}

n ( A ) = 8 and n ( B ) = 7

(A ∪B) = {1,2,3,5,7,9,11,13} ∪{1,2,4,6,8,12,13} = {1,2,3,4,5,6,7,8,9,11,12,13}

n (A ∪B) = 12

( A ∩B ) = {1,2,3,5,7,9,11,13} ∩{1,2 4,6,8,12,13} = {1,2,13}

n ( A ∩B ) = 3

∴ n ( A ∪B) + n ( A ∩B ) = 12 + 3 = 15

n ( A ) + n ( B ) = 8 + 7 = 15

Hence we proved that n ( A ∪ B ) + n ( A ∩B ) = n ( A ) + n ( B ).