Question

Find the correct answer ?

$A-B=A\cap B^{\prime }=B^{\prime }-A^{\prime }$. True or false?
If true enter 1 else 0.

Answer 1

Let U be the universal set.
Then
$A\cap B^{\prime }$
$=A\cap (U-B)$
$=(A\cap U)-A\cap B$
$=A-(A\cap B)$
$=A-B$...(i)
Now
$B^{\prime }-A^{\prime }$
$=(U-B)-(U-A)$
$=A-B$ ...(ii)
Hence
$A-B=A\cap B^{\prime }=B^{\prime }-A^{\prime }$