Addendum to CPS 430/542 Homework #4

1. (5 points) Consider the following sets of FDs over the relation R(A, B, C):
   • F₁ = {A → B, B → C}
   • F₂ = {A → B, A → C}
   • F₃ = {A → B, A B → C}
   
   Identify all sets above which follow from a) F₁ b) F₂, and c) F₃. Which pairs of these sets of FDs (F₁ and F₂, F₂ and F₃, and F₁ and F₃) are equivalent to each other?
   
   
2. (5 points) Consider the following set of FDs over the relation Widgets(source, destination, volume, weight):
   
   source volume → weight
   destination → weight
   source volume → destination
   
   
   1. Give a minimal set of FDs equivalent to the set above.
   2. Give one key for the relation Widgets and prove it is a key.
   3. Any there any other keys? Give reasons.