Question

prove that A-(A intersection B)= A-B

Answer 1

here is the ans for the qn.

Answer 2

To prove:

$A-(A \cap B)=A-B$

As we know that,  

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$

The above equation can be applicable for any two sets.  

So,

$\begin{array}{l}{n(A \cup B)-n(B)=n(A)-n(A \cap B)} \\ {n(A)-n(A \cap B)=n(A \cup B)-n(B)}\end{array}$

If B is a proper subset of A, then n(A∪B) is equal to A.  

$n(A)-n(A \cap B)=n(A-B)$

$\bold{A-(A \cap B)=A-B}$

Hence proved.

In some special case A=B, which is the “proper subset of B” is A,

$A-B=A \cap B-B$.