Question

Let U=(4, 5, 6, 7, 8, 9, 10, 11), A = (s, 7, 9), B following. (Enter your answers as a comma-separated list.) {4, 5, 8, 11), and C = (4, 6, 10). Find the (A U B) n (Bn C')

Answer 1

Answer: (A U B) n (B n C') = {5, 8, 11}.

Step-by-step explanation: We are given the following sets :

U = {4, 5, 6, 7, 8, 9, 10, 11},

A = {5, 7, 9},

B = {4, 5, 8, 11}

and

C = {4, 6, 10}.

We are to find the following :

(A U B) n (B n C')

We know that for any two sets A and B,

A ∪ B contains all the elements present in set A or set B or both,

A ∩ B contains all the elements present in both A and B,

A - B contains all those elements which are present in A but not B

and

A' contains all the elements present in the universal set U but not A.

We will be suing the following rule of set of theory :

A ∩ B' = A - B.

Therefore, we have

`(A\cup B)\cap(B\cap C')\\\\=(A\cup B)\cap (B-C)\\\\=(\{5,7,9\}\cup\{4,5,8,11\})\cap (\{4,5,8,11\}-\{4,6,10\})\\\\=\{4,5,7,8,9,11\}\cap\{5,8,11\}\\\\=\{5,8,11\}.`

Thus, (A U B) n (B n C') = {5, 8, 11}.