Express the following Boolean expressions in simpler form; that is, use tewer operators. X is ah inb (a) !(x == 2)

Draw the truth table of the boolean expression X = A.B.C + A'.C' + A'.B'. Do, not simplify the expression and draw the truth table directly.

(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression s: 2, r'-0. ((r')). r), n -n +½. (b) Given a regular expression 7; = a(ab)* +b°a*, r, = (b + a)* +a*, find L(;) and L(r,), the languages associated with i and r3, respective ly. (c) Find a regular expression r such that L(r) is the same as L = {b"ab",(ba)* : n, m2 0,h2 1}. %3D

Write an expression using boolean variables a and b that evaluates to true when only one of a and b is true, and that is false if a and b are both false or both true. (This is also called an exclusive or.)