Question

for any sets A and B prove that A-B=A intersection B'

Answer 1

A - B means everything in A except for anything in $A\cap B$

Let X is an arbitrary element of A - B
it means , $X\in A-B$
$\implies x\in A$ and $x\notin B$
$\implies x\in A$ and $x\in B'$
$\implies x\in A\cap B'$
$\implies A-B=A\cap B'$

similarly, Let y is an arbitrary element of $A\cap B'$
then, $y\in A\cap B'$
$\implies y\in A$ and $y\in B'$
$\implies y\in A$ and $y\notin B$
$\implies y\in A-B$
$\implies A\cap B'=A-B$
hence proved//

Answer 2

Answer:it is given to prove...

Go through it..

Step-by-step explanation:

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 ☆]