Question

If $U=\{1,2,3,4,5,6,7,8,9,10\}$
$A=\{1,2,6,7\}$
$B=\{3,4,5,1\}$
$C=\{6,7,8,4\}$
Find
(i)${\left(A\cup B\right)}^{\prime }\cap {\left(A\cup C\right)}^{\prime }$
(ii)$(C^{\prime }-A)-\left(A-C\right)$
(iii)$\left(B\cap C\right)\cup \left(A\cap C\right)$
(iv)${\left(A\cup B\cup C\right)}^{\prime }$

Answer 1

$1.A\cup B=\{1,2,3,4,5,6,7\}$

$⟹(A\cup B{)}^{{}^{\prime }}=\{8,9,10\}$

$A\cup C=\{1,2,4,6,7,8\}$

$(A\cup C{)}^{{}^{\prime }}=\{3,5,9,10\}$

$⟹(A\cup B{)}^{{}^{\prime }}\cap (A\cup C{)}^{{}^{\prime }}=\{9,10\}$

$2.C^{{}^{\prime }}=\{1,2,3,5,9,10\}$

$C^{{}^{\prime }}-A=\{3,5,9,10\}$

$A-C=\{1,2\}$

$(C^{{}^{\prime }}-A)-(A-C)=\{3,5,9,10\}$

$3.B\cap C=\left\{4\right\}$

$A\cap C=\{6,7\}$

$(B\cap C)\cup (A\cap C)=\{4,6,7\}$

$4.A\cup B\cup C=\{1,2,3,4,5,6,7,8\}$

$(A\cup B\cup C{)}^{{}^{\prime }}=\{9,10\}$