Question

. Using the properties of set prove A-(A-B) = A∩B​

Answer 1

${ \boxed{ \bold \red{A}}}{ \boxed{ \bold \green{N}}}{ \boxed{ \bold \blue{S}}}{ \boxed{{{ \bold{W}}}}}{ \boxed {\bold \pink{E}}}{ \boxed {\bold \purple{R}}}$

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