Question

Given { a, b , c , d, e}, B = { a, e, i, o, u} and C ={ c, d, e, u}.
(i) Show that $A\setminus (B\setminus C)\ne (A\setminus B)\setminus C$.
(ii) Verify (i) using Venn diagram.

Answer 1

$B$ \ $C=${$a,i,o$}

$A$ \ $(B$ \ $C)=${$b,c,d,e$} $-\left(i\right)$

$A$ \ $B=${$b,c,d$}

$(A$ \ $B)$ \ $C=${$b$} $-\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$ $A$ \ $(B$ \ $C)\ne (A$ \ $B)$ \ $C$

We can also see the result from Venn's diagram