Sarthaks Test
0 votes
1.3k views
in Mathematics by (7.9k points)

Use the properties of sets to prove that for all the sets A and B

A – (A ∩ B) = A – B

1 Answer

0 votes
by (13.1k points)
selected by
 
Best answer

We have

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

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...