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DBMS Losless join

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R is divided into R1 and R2 ,but since there is no common attribute in R1 and R2, so it should form lossy join,as for loseless join the common attribute has to be key in one of the table.But here the image above,it is comming as loseless join.Can someone please check?

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$R(X,Y,Z,W) is\ decomposed\ into \\ R_1(X,Y)\\ R_2(Y,Z)\\ R_3(Y,W).\\The\ FDs\ are\ :\\ X -> Y,\\ Z->Y,\\ Y->W \\ Find\ whether\ the\ decomposition\ is\ lossless\ or\ lossy\ ?$
$R(X,Y,Z,W) is\ decomposed\ into \\ R_1(X,Y)\\ R_2(Y,Z)\\ R_3(Y,W).\\The\ FDs\ are\ :\\ X - Y,\\ Z->Y,\\ Y->W \\ Find\ whether\ the\ decomposition\ is\ lossless\ or\ ...
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