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DBMS Losless join

in Databases
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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?

in Databases
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@Rahul,

lossless join is never checked by seeing particular instance...

what if in future, some tupple (a,b,d,6,9) is added, then it will become lossy....

therefore lossless join is never checked for a particular instance, it is checked for general schema taking functional dependecy in consideraion

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Got that.Thanks a lot
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