4. Perform the chase test for the lossless join property for the universal relation R(A₁, A₂, A₃, A₄), and the decomposition D and set of functional dependencies F given below:

D = { R₁(A₁, A₂) , R₂(A₁, A₃) , R₃(A₂, A₃, A₄) }

F = { A₂ --> A₄ , A₃ --> A₂ }

A. Show the initial state of the matrix S, and show each step of your work as you modify the matrix using the functional dependencies. (That is, dont just show me the final state of the matrix each time you change it, show the change, and show which functional dependency you applied to make the change)

B. Does the decomposition D have the lossless join property? Explain why or why not in terms of the final state of the matrix S.