Question

U={4,7,8,10,11,12,15,16}, A = {7,8,11,12}, B = {4,8,12,15} then verify (AUB)’ =A’∩ B’​

Answer 1

Step-by-step explanation:

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Answer 2

Given :-

• U={4,7,8,10,11,12,15,16}, A = {7,8,11,12}, B = {4,8,12,15}

To find :-

• (A U B)' = A' ∩ B'

Solution :-

• U = {4, 7, 8, 10, 11, 12, 15, 16}

• A = {7, 8, 11, 12}

• B = {4, 8, 12, 15}

→ LHS = (A U B)'

Firstly we have to find out (A U B)

→ A U B = {4, 7, 8, 11, 12, 15}

→ (A U B)' = {10, 16}

→ RHS = A' ∩ B'

Firstly we have to find out A' and B'

→ A' = {4, 10, 15, 16}

→ B' = {7, 10, 11, 16}

Now,

→ A' ∩ B' = {10, 16}

• Hence, LHS = RHS

• (A U B)' = A' ∩ B'

• Therefore verified