3. The objective of this problem is to create a function that adds two 2-digit binary numbers using the logical operation and the operator . Use the notation x2x1 and y2y1 for the two summands (the xs and ys are digits), and z3z2z1 for the sum. I suggest creating the function so that the input is the ordered quadruple (x2, x1, y2, y1) and the output is the ordered triple (z3, z2, z1). The variables (x1, . . . , z3) are elements of M interpreted as though each is equal to 1 or 0 depending on whether they are true or false, respectively. So if you name your function add, then add : M M M M M M M, that is add : M4 M3 . 4. Turn the logical system (M, , , , = , =, ,) into a purely algebraic system over (Z2, +, ) with, for x M, (x) = 0 if x is true and (x) = 1 if x is false. Use the logical system to show that any statement of the form [P ((P = Q) Q)] = P is a tautolog