13. Although a Boolean variable for a combinational circuit can have only two values, 1 or 0, Boolean algebra can describe a system where a variable can have one of four possible values—0, 1, A, or B. Such a system corresponds to the description of subsets of {a, b}

where 1 = {a, b} (the universal set), A = {a}, B = {b}, and 0 = {} (the empty set). The truth tables for two-input AND and OR operations have 16 entries instead of 4, and the truth table for the complement has 4 entries instead of 2. Construct the truth table for the following:

(a) AND

(b) OR

(c) the complement