Consider a relation R that has three attributes ABC. It is decom-posed into relations R1 with attributes AB and R2 with attributes BC.
1. State the definition of a lossless-join decomposition with respect to this example. Answer this question concisely by writing a relational algebra equation involving R, R1, and R2.
2. If you are given the following instances of R1 and R2, what can you say about the instance of R from which these were obtained? Answer this question by listing tuples that are de?nitely in R and tuples that are possibly in R.
Instance of R1 = {(5,1), (6,1)} Instance of R2 = {(1,8), (1,9)}
Can you say that attribute B de?nitely is or is not a key for R?