Question

can anyone solve this question ?? ​

Answer 1

Answer:

From the question it is given that,

ξ = {natural numbers between 10 and 40}

ξ = {11,12, 13, 14, 15, …., 39}

ξ is a universal set and A and B are subsets of ξ.

Then, the elements of A and B are to be taken only from ξ.

A = {multiples of 5}

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

B = {multiples of 6}

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

(i) A ∪ B = {15, 20, 25, 30, 35, 40} ∪ {12, 18, 24, 30, 36}

A ∪ B = {15, 20, 25, 30, 35, 12, 18, 24, 36}

A ∩ B = {30}

(ii) n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

n(A ∪ B) = 5

n(A) = 5

n(B) = 5

n(A ∩ B) = 1

Then, n(A) + n(B) – n(A ∩ B) = 5 + 5 – 1 = 9

By comparing the results,

9 = 9

Therefore, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

Step-by-step explanation:

Hope it helps :)