Let S be a subset of a universal set U$.$ The characteristic function fS of S is the

function f : U $->\{0,1\}$ defined by fS$($x$)=1$ if x in S and fS$($x$)=0$ if x $/$ in S$.$ So for

example, if U $=\{0,1,2,3\}$ and S $=\{0,3\}$ then fS$(0)=1,$ fS$(1)=0,$ fS$(2)=0,$ and

fS$(3)=1.$

Let A $$ U and B $$ U$.$ Show that fA$\backslash$cap B$($x$)=$ fA$($x$)$ fB$($x$).$