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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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