Let A,B,C be three sets. Show that A intersect (B union C) = (A intersect B) union (A intersect C)
You need to prove distributive law of sets such that:
`Ann (BUC) = (AnnB)U(AnnC)`
You need to prove that (by definition U)
=> `(x in A ^^ x in B) vv (x in A ^^ x in C) ` (use distibution from logic equivalence)
=>`(x in Ann B) vv (x in A nn C) ` (use definition of `nn` )
=>`(x in Ann B)U (x in A nn C)` (use definition of U).
Hence, using logic equivalences yields the distributive law of sets such that A`nn` (BUC) `= (AnnB)U(AnnC)` .