Question

If A = { 1,2,3,4} , B = { 2,4,6,8} ,
C = { 3,4,5,6} and universal set U = { x | x € N, x < 10} , verify
(A n B)' = A' U B'​

Answer 1

Step-by-step explanation:

(A n B)={2,4}

(A n B)'=U -- (A n B)

(A n B)'={1,3,5,6,7,8,9}

A' U B' = (U-A) U (U-B)

A' U B' = {1,3,5,6,7,8,9}

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Answer 2

Answer:

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Step-by-step explanation:

Step-1:Prove using suitable formula of sets.

It is given that,

A∪B = A∪C …(1)

A∩B = A∩C…(2)

Taking  ’∩ C’ on both sides in equation (1)

(A∪B)∩C = (A∪C)∩C

We know that,

(A∪B)∩C = (A∩C)∪(B∩C) and (A∪C)∩C = C

So,

(A∩C)∪(B∩C)=C

(A∩B)∪(B∩C)=C…(3)[From(2))

Again,

Taking  ’∩ B’ on both side in equation (1)

(A∪B)∩B = (A∪C)∩B

B = (A∩B)∪(C∩B)

B = (A∩B)∪(B∩C)

B = C[From (3)]

Hence, proved.