Question

6. If & = {natural numbers between 10 and 40}, A = {multiples of 5} and B = {multiples of 6}, then (i) find A U B and An B. (ii) verify that n(A U B) = n(A) + n(B) – n(A n B). ​

Answer 1

= {11, 12, 13, 14, 15, . ,39}

is a universal set and A and B are subsets of Then, the elements of A and

Bare to be taken only from

A = { multiples of 5}

A = {15, 20, 25, 30, 35}

B = { multiples of 6}

B = {12, 18, 24, 30, 36}

(i) AUB={15, 20, 25, 30, 35, 40} U

{12, 18, 24, 30, 36}

AUB =

{15, 20, 25, 30, 35, 12, 18, 24, 36} AnB = {30}

(ii) n(AUB)=n(A)+n(B)−n(An

B) n(AUB) = 5

n(A) = 5

n(B) = 5

n(AnB) = 1

Then, n(A) + n(B) – n(A^B) = 5 + -

5-1=9

By comparing the results, 9 = 9

Therefore, n(AUB) = n(A) + n(B) –

n(An B)