Question: 2. Given R(A, B, C) and S(B, D), prove or disprove the following RA propositions. Assume all columns have the same domain (e.g. strings). (a)

2. Given R(A, B, C) and S(B, D), prove or disprove the following RA propositions. Assume all columns have the same domain (e.g. strings).

(a) B,C(R) S = B,C,D(R S).

(b) If A B holds for instances of R, then AB(A,c (R)) S = B,C(R) S.

(c) If A B holds for instances of R, then A,B (R) A,c (R) = R

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