erform the test for the non-additive join property (lossless join) for the relation R(A₁, A₂, A₃, A₄, A₅), and the decompositions D_a, D_b, D_c, D_d and set of functional dependencies F given below. You can ignore attributes that are not mentioned in each particular subsection (e.g., you can ignore absence of A₄ in D_d, just test the join between R₁ and R₂):

D_a = { R₁(A₁, A₂) , R₂(A₃, A₄, A₅) }

D_b = { R₁(A₃, A₄) , R₂(A₄, A₅) }

D_c = { R₁(A₁, A₅) , R₂(A₄, A₅) }

D_d = { R₁(A₁, A₂, A₃) , R₂(A₁, A₂, A₅) }

F = { A₁A₄ , A₄A₅ , A₃A₄ }

a. Does the decomposition D_a have the non-additive join property? Explain why or why not.

b. Does the decomposition D_b have the non-additive join property? Explain why or why not.

c. Does the decomposition D_c have the non-additive join property? Explain why or why not.

d. Does the decomposition D_d have the non-additive join property? Explain why or why not.