Consider a relation R ( A, B, C, D, E, G, H, I, J, K ) and its FD set F = { A -gt; BC, E-gt; AD, BD -gt; E, CE -gt; DH, H-gt; G, EI -gt; J} 1)

Consider a relation R(A, B, C, D, E, G, H, I, J, K) and its FD set F = {A -> BC, E-> AD, BD -> E, CE -> DH, H-> G, EI -> J}

1) Check if C -> J ∈ (is an element of) F+

2) Find a minimal cover Fm for F.

3) Regarding F, is the decomposition R1 = {ABCDE}, R2 = {EGH}, R3 = {EIJK} of R lossless-join? Please justify your answer.

4) List at least 5 super-keys for R.

5) Is it possible to decompose R into a collection of BCNF relations and ensure the decomposition is dependency-preserving and lossless-join? Please justify your answers.