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n-A-7-n-A-B-4-3n-A-B-n-B-n-B-A-




Question Number 169432 by mathlove last updated on 30/Apr/22
n(A)=7  n(A∩B)=4  3n(A−B)=n(B)  n(B−A)=?
$${n}\left({A}\right)=\mathrm{7} \\ $$$${n}\left({A}\cap{B}\right)=\mathrm{4} \\ $$$$\mathrm{3}{n}\left({A}−{B}\right)={n}\left({B}\right) \\ $$$${n}\left({B}−{A}\right)=? \\ $$
Answered by blackmamba last updated on 30/Apr/22
 n(A−B)= n(A)−n(A∩B)  ⇒3(7−4)=n(B) ; n(B)=9  n(B−A)=n(B)−n(A∩B)=9−4=5
$$\:{n}\left({A}−{B}\right)=\:{n}\left({A}\right)−{n}\left({A}\cap{B}\right) \\ $$$$\Rightarrow\mathrm{3}\left(\mathrm{7}−\mathrm{4}\right)={n}\left({B}\right)\:;\:{n}\left({B}\right)=\mathrm{9} \\ $$$${n}\left({B}−{A}\right)={n}\left({B}\right)−{n}\left({A}\cap{B}\right)=\mathrm{9}−\mathrm{4}=\mathrm{5} \\ $$

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