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′.
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Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

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′.

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️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′

$\Large\mathcal\green{FOLLOW \: ME}$

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Answer 2

Answer:

➡️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′✔

Step-by-step explanation:

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