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If-n-A-B-32-n-B-12-and-n-A-B-5-then-n-A-




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

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