Question

Use the properties of sets to prove that for all the sets A and B, A – (A ∩ B) = A – B​

Answer 1

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

Use the properties of sets to prove that for all the sets A and B, A – (A ∩ B) = A – B

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

➡️A – (A ∩ B) = A ∩ (A ∩ B)′ (since A – B = A ∩ B′)

➡️= A ∩ (A′ ∪ B′) [by De Morgan’s law)

➡️= (A∩A′) ∪ (A∩ B′) [by distributive law]

➡️= φ ∪ (A ∩ B′)

➡️= A ∩ B′ = A – B

➡️Hence proved that A – (A ∩ B) = A – B.

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

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Answer 2

Answer:

➡️A – (A ∩ B) = A ∩ (A ∩ B)′ (since A – B = A ∩ B′)

➡️= A ∩ (A′ ∪ B′) [by De Morgan’s law)

➡️= (A∩A′) ∪ (A∩ B′) [by distributive law]

➡️= φ ∪ (A ∩ B′)

➡️= A ∩ B′ = A – B

➡️Hence proved that A – (A ∩ B) = A – B.✔

Step-by-step explanation:

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