Prove the following statement in the format A=B without using element-chase format: A-(A-B) = A∩B

Answer 1

A - (A - B) =

A - (A intersect B') = <-- theorem of set subtraction

A intersect (A intersect B')' = <-- theorem of set subtraction

A intersect (A' U B) = <-- DeMorgan's

(A intersect A') U (A intersect B) = <-- Distributive

empty set U (A intersect B) =

A intersect B