Question

if p= {x:x is a factor of 6}
q= { x x is a prime number, a <8}
R= {x:x is a whole number between
2.8 and 8.2}
then find (i) P- (QUR) (:) (p-q)intersection (P-R)
What do you observe ?​

Answer 1

$\textbf{Given:}$

$P=\{x|\;\text{x is a factor of 6}\}$

$Q=\{x|\;\text{x is a prime number and x < 8}\}$

$R=\{x|\;\text{x is a whole number between 2.8 and 8.2}\}$

$\textbf{To find:}$

$(i)\;P-(Q{\cup}R)$

$(ii)\;(P-Q){\cap}(P-R)$

$P=\{1,2,3,6\}$

$Q=\{2,3,5,7\}$

$R=\{3,4,5,6,7,8\}$

$(i)$

$Q{\cup}R=\{2,3,4,5,6,7,8\}$

$\implies\bf\,P-Q{\cup}R=\{1\}$

$(ii)$

$P-Q=\{1,6\}$

$P-R=\{1,2\}$

$\implies\bf(P-Q){\cap}(P-R)=\{1\}$

$\text{From (i) and (ii), it is clear that}$

$\bf\,P-(Q{\cup}R)=(P-Q){\cap}(P-R)$

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