Question Number 7710 by abdel19599@yahoo.com last updated on 11/Sep/16
$$\mathrm{If}\:{n}\left(\mathrm{A}\cup\mathrm{B}\right)=\mathrm{32},\:{n}\left(\mathrm{B}\right)=\mathrm{12}\:\mathrm{and}\:{n}\left(\mathrm{A}\cap\mathrm{B}\right)=\mathrm{5} \\ $$$$\mathrm{then}\:{n}\left(\mathrm{A}\right)=? \\ $$
Answered by Rasheed Soomro last updated on 11/Sep/16
$$\:{n}\left(\mathrm{A}\cup\mathrm{B}\right)={n}\left({A}\right)+{n}\left({B}\right)−{n}\left(\mathrm{A}\cap\mathrm{B}\right) \\ $$$$\mathrm{32}={n}\left({A}\right)+\mathrm{12}−\mathrm{5} \\ $$$${n}\left({A}\right)=\mathrm{32}−\mathrm{7}=\mathrm{25} \\ $$