Question

Let A = \{a, b, c, d, e, f, g, x, y, z \}, B = \{ 1, 2, c, d, e\} and C = \{ d, e, f, g, 2, y\}.
Verify $A\setminus (B\cup C)=(A\setminus B)\cap (A\setminus C)$.

Answer 1

$B\cup C=${$1,2,c,d,e,f,g,2,y$}

$A$ \ $(B\cup C)=${$a,b,x,z$} $-\left(i\right)$

$A$ \ $B=${$a,b,f,g,x,y,z$}

$A$ \ $C=${$a,b,c,x,z$}

$(A$ \ $B)\cap (A$ \ $C)=${$a,b,x,z$} $-\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$ we verify $A$ \ $(B\cup C)=(A$ \ $B)\cap (A$ \ $C)$