Prove (A-B)=(A intersection B)

Question

Question of sets

Answer 1

A-B means everything in A except for anything in A∩B

A-B=A∩B^c (A intersect B complement)

pick an element x

let x∈(A-B)

therefore x∈A but x∉B

x∉B means x∈B^c

x∈A and x∈B^c

x∈(A∩B^c)

x∈(A-B)

therefore A-B=A∩B^c