Question

Let A = {a, b, c, d} B = {a, c , e} and C ={a, e}

(i) Show that $A\cap (B\cap C)=(A\cap B)\cap C$.
(ii) Verify (i) using Venn diagram.

Answer 1

$B\cap C=${$a,e$}

$A\cap (B\cap C)=${$a$} $-\left(i\right)$

$A\cap B=${$a,c$}

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

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

Venn diagram also proves the equation right.