Question

1) If $U=1,2,3,4,5,6,7,8,9,10,$
$A=1,2,3,5$, $B=2,4,6,7$ $\text{and}C=2,3,4,8.\text{Then}(B\cup C{)}^{\prime }\text{is}$


2) If $U=1,2,3,4,5,6,7,8,9,10$, $A=1,2,3,5$, $B=2,4,6,7$ $\text{and}C=2,3,4,8.\text{Then}(C-A{)}^{\prime }\text{is}$

• A. {1, 2, 3, 5, 6, 7, 9, 10}
• B. {1, 5, 9, 10}

Answer 1

Answer: (A), (B)

Given : $U=\{1,2,3,4,5,6,7,8,9,10\}$

$A=\{1,2,3,5\},$

$B=\{2,4,6,7\},$

$C=\{2,3,4,8,\}$

$(B\cup C{)}^{\prime }={\{2,3,4,6,7,8\}}^{\prime }=\{1,5,9,10\}$

$[\because A^{\prime }=U-A]$

Hence, $(B\cup C{)}^{\prime }=\{1,5,9,10\}$

2) $U=\{1,2,3,4,5,6,7,8,9,10\}$

$A=\{1,2,3,5\},$

$B=\{2,4,6,7\},$

$C=\{2,3,4,8\}$

$(C-A{)}^{\prime }={\{4,8\}}^{\prime }$

$[\because C-A=x|x\in C\text{and}x\notin A]$

$\Rightarrow (C-A{)}^{\prime }=\{1,2,3,5,6,7,9,10\}[\because A^{\prime }=U-A]$

Hence, $(C-A{)}^{\prime }=\{1,2,3,5,6,7,9,10\}$