Question

prove that for any set a and b a-b=a∩b'​

Answer 1

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

A-B=A∩Bc (A intersect B complement)

pick an element x

let x∈(A-B)

therefore x∈A but x∉B

x∉B means x∈Bc

x∈A and x∈Bc

x∈(A∩Bc)

x∈(A-B)

therefore A-B=A∩Bc