Use the properties of sets to prove that for all the sets A and B, A – (A ∩ B) = A – B
Use the properties of sets to prove that for all the sets A and B, A – (A ∩ B) = A – B
Harsh Singh Chauhan , 5 Years ago
Grade 12th pass
Analytical Geometry> Use the properties of sets to prove that ...
1 AnswersHarshit Singh
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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.
Thanks
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.
Thanks
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