Question Number 135634 by oustmuchiya@gmail.com last updated on 14/Mar/21
Answered by physicstutes last updated on 14/Mar/21
$$\left({i}\right)\:{n}\left({B}\right)\:=\:\mathrm{8}\:+\:\mathrm{5}\:+\:{x}−\mathrm{4}\:=\:\mathrm{11}\:+\:{x} \\ $$$$\:{n}\left(\:{B}\cup{C}\right)\:=\:\mathrm{8}+\:{x}−\mathrm{4}\:+\:\mathrm{5}\:+\:\mathrm{2}{y}\:=\:\mathrm{9}\:+\:{x}\:+\:\mathrm{2}{y} \\ $$$$\Rightarrow\:\:\mathrm{11}\:+\:{x}\:=\:\mathrm{9}\:+{x}\:+\:\mathrm{2}{y}\:\:\Rightarrow\:\:\:\mathrm{2}\:=\:\mathrm{2}{y}\:\Rightarrow\:{y}\:=\:\mathrm{1} \\ $$$$\left({ii}\right)\:{n}\left({C}\right)\:=\:\mathrm{5}\:+\:\mathrm{2}{y}\: \\ $$$$\mathrm{and}\:{n}\left({A}\right)\:=\:\mathrm{15} \\ $$$$\Rightarrow\:\mathrm{5}\:+\:\mathrm{2}{y}\:=\:\mathrm{15}\:\Rightarrow\:\mathrm{2}{y}\:=\:\mathrm{10}\:,\:{y}\:=\:\mathrm{5}\:\left(\mathrm{error}\:\mathrm{in}\:\mathrm{question}\:\mathrm{as}\:\mathrm{there}\:\mathrm{is}\:\mathrm{inconsistency}\right) \\ $$$$ \\ $$