Question

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.

Find A′, B′, A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′∩ B′.​

Answer 1

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Given,

U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}

A′ = {1, 4, 5, 6}

B′ = { 1, 2, 6 }.

Hence, A′ ∩ B′ = { 1, 6 }

Also A ∪ B = { 2, 3, 4, 5 }

(A ∪ B)′ = { 1, 6 }

Therefore, ( A ∪ B )′ = { 1, 6 } = A′ ∩ B′

Answer 2

Step-by-step explanation:

A' = {1,4,5,6}

B' = {1,2,6}

A' ∩ B' = {1,6} ----------------(1)

A U B = {2,3,4,5}

(A U B)' = {1,6} ---------------- (2)

thus, from (1) & (2)

(A U B)' = A' ∩ B'