(For students having some knowledge of the laws of set theory) For a set S, (S) be the col...

(For students having some knowledge of the laws of set theory) For a set S, (S) be the collection of all subsets of S. Let binary operations + and • on (S) be defined by

A + B = (A ∪ B) - (A ∩ B) = {x | X ∊ A or X ∊ B but X ∉ (A ∩ B)}

and

A • B = A ∩ B

for A, B ∊ (S).

a. Give the tables for + and • for (S), where S = {a, b}. [Hint: (S) has four elements.J

b. Show that for any set S, 〈S), +, •〉 is a Boolean ring (see Exercise 55).