Use Venn diagrams(a) to simplify the expressions (E  F)(E  Fc);(b) to prove DeMorgan’s law...

Use Venn diagrams

(a) to simplify the expressions (E  F)(E  Fc);

(b) to prove DeMorgan’s laws for events E and F. [That is, prove (E  F)c = ECFC, and (EF)C = Ec  Fc.]