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if-x-and-y-are-two-sets-such-that-n-x-17-n-y-23-and-n-X-Y-38-find-n-X-Y-




Question Number 9423 by Rohit kumar last updated on 08/Dec/16
if x and y are two sets such that n(x)  =17 , n(y)=23 and n(X∪Y) =38,  find n(X∪Y).
$${if}\:{x}\:{and}\:{y}\:{are}\:{two}\:{sets}\:{such}\:{that}\:{n}\left({x}\right) \\ $$$$=\mathrm{17}\:,\:{n}\left({y}\right)=\mathrm{23}\:{and}\:{n}\left({X}\cup{Y}\right)\:=\mathrm{38}, \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{n}}\left({X}\cup{Y}\right). \\ $$
Commented by sandy_suhendra last updated on 08/Dec/16
do you mean n(X∩Y) ?
$$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{n}\left(\mathrm{X}\cap\mathrm{Y}\right)\:? \\ $$
Commented by Rohit kumar last updated on 08/Dec/16
x∪y
$${x}\cup{y} \\ $$$$ \\ $$
Commented by RasheedSoomro last updated on 08/Dec/16
n(x∪y)=38 (Given)
$$\mathrm{n}\left({x}\cup{y}\right)=\mathrm{38}\:\left(\mathrm{Given}\right) \\ $$
Answered by sandy_suhendra last updated on 08/Dec/16
n(X∪Y)=n(X)+n(Y)−n(X∩Y)  where ∪=unions and ∩=intersections
$$\mathrm{n}\left(\mathrm{X}\cup\mathrm{Y}\right)=\mathrm{n}\left(\mathrm{X}\right)+\mathrm{n}\left(\mathrm{Y}\right)−\mathrm{n}\left(\mathrm{X}\cap\mathrm{Y}\right) \\ $$$$\mathrm{where}\:\cup=\mathrm{unions}\:\mathrm{and}\:\cap=\mathrm{intersections} \\ $$

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