Question-166542

Question Number 166542 by abdurehime last updated on 22/Feb/22

Answered by Rasheed.Sindhi last updated on 22/Feb/22

n(A)=(2x+y)+(x+y)=3x+2y=13 n(B)=(3y−x)+(x+y)=4y=8 y=8/4=2⇒3x+2(2)=13⇒x=3 (a) n(A∪B)=(2x+y)+(x+y)+(3y−x) =2x+5y=2(3)+5(2)=16 (b) n(U)=16+(2x−y)=16+2(3)−2=20 (c) n(B−A)=3y−x=3(2)−3=3 (d) n(A∩B ′ )=? n(A∩B ′)=n(A−B)=2x+y=2(3)+2=8

$${n}\left({A}\right)=\left(\mathrm{2}{x}+{y}\right)+\left({x}+{y}\right)=\mathrm{3}{x}+\mathrm{2}{y}=\mathrm{13} \\ $$$${n}\left({B}\right)=\left(\mathrm{3}{y}−{x}\right)+\left({x}+{y}\right)=\mathrm{4}{y}=\mathrm{8} \\ $$$${y}=\mathrm{8}/\mathrm{4}=\mathrm{2}\Rightarrow\mathrm{3}{x}+\mathrm{2}\left(\mathrm{2}\right)=\mathrm{13}\Rightarrow{x}=\mathrm{3} \\ $$$$\left({a}\right)\:{n}\left({A}\cup{B}\right)=\left(\mathrm{2}{x}+{y}\right)+\left({x}+{y}\right)+\left(\mathrm{3}{y}−{x}\right) \\ $$$$\:\:\:\:\:\:\:=\mathrm{2}{x}+\mathrm{5}{y}=\mathrm{2}\left(\mathrm{3}\right)+\mathrm{5}\left(\mathrm{2}\right)=\mathrm{16} \\ $$$$\left({b}\right)\:{n}\left({U}\right)=\mathrm{16}+\left(\mathrm{2}{x}−{y}\right)=\mathrm{16}+\mathrm{2}\left(\mathrm{3}\right)−\mathrm{2}=\mathrm{20} \\ $$$$\left({c}\right)\:{n}\left({B}−{A}\right)=\mathrm{3}{y}−{x}=\mathrm{3}\left(\mathrm{2}\right)−\mathrm{3}=\mathrm{3} \\ $$$$\left({d}\right)\:{n}\left({A}\cap{B}\:'\:\right)=? \\ $$$$\:\:\:\:{n}\left({A}\cap{B}\:'\right)={n}\left({A}−{B}\right)=\mathrm{2}{x}+{y}=\mathrm{2}\left(\mathrm{3}\right)+\mathrm{2}=\mathrm{8}\:\:\:\:\: \\ $$

Commented by abdurehime last updated on 22/Feb/22