ξ = {a,b,c,d,e,i,o,r,s,t,u,v} A = {c,e,d,a,r} B = {v,i,c,t,o,r,a} Find A ∩ B Answer ___ A' ∩ B' Answer ___ Use set notation to describe the shaded region. Answer ___

1. Identify the common elements in $A$ and $B$.

$A=\{c,e,d,a,r\}$ and $B=\{v,i,c,t,o,r,a\}$.

The elements that appear in both sets are $c$, $a$ and $r$.

Hence,
$A\cap B=\{a,c,r\}.$

1. Find the elements that are not in either $A$ or $B$.

$A' \cap B'$ means the elements in $\xi$ that are not in $A$ and not in $B$.

Elements appearing in $A$ or $B$ are
$\{a,c,d,e,i,o,r,t,v\}$.

From $\xi=\{a,b,c,d,e,i,o,r,s,t,u,v\}$, the elements not in either set are
$\{b,s,u\}$.