Question

Prove that : A – (A – B)= A ∩ B​

Answer 1

$\huge\bold{\underline{\sf{\red{Solution:-}}}}$

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

A-B=A∩B' (A intersect B complement)

pick an element x

let x∈(A-B)

therefore x∈A but x∉B

x∉B means x∈B'

x∈A and x∈B'

x∈(A∩B')

x∈(A-B)

therefore A-B=A∩B'

Here we have LHS=RHS.[⭐Hence proved ⭐]