Find a minimal cover of the following set of FDs: AB ? CD, BC ? FG , A ? G, G ? B, C ? G. Is the decomposition of ABCDFG into ABCD and ACFG lossless? Explain.
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Splitting the RHSs replaces the ?rst two FDs with: AB ? C , AB ? D, BC ? F , BC ? G.
Since we can derive A ? B,wecandeleteB from the LHSs of the ?rst two of these: A ? C , A ? D. Because of C ? G ? B, we can eliminate B from BC ? G and BC ? F . We are left with: A ? C , A ? D, C ? F , C ? G, A ? G, G ? B.
A ? G is redundant, so we are left with A ? C , A ? D, C ? F , C ? G, G ? B. The decomposition of ABCDFG into ABCD and ACFG is lossless because AC = ABCD ? ACFG and AC ? FG is implied by the given FDs.
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Fill in the blank(s) with correct word
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