I would like help in solving 12.1, 12.2 b, 12.4 a, 12.5, and 12.7.

12.1 12.2 12.3 Construct a truth table for the following Boolean expressions: a. ABC + ABC b. ABC + ABC + ABC c. A(BC + BC) d. (A + B) (A +C)(A+B) Simplify the following expressions according to the commutative law: a. A B+BA+C.D.E+C.D. E+E CD b. A.B+A.C+BA c. (LMN) (A B) (C.D.E) (MNL) d. F.(K+R) +S.V+W.X+V.S+X.W+(R+K). F Apply DeMorgan's theorem to the following equations: a. F= V +A+L b. F=+B+C+D Simplify the following expressions: a. A=ST+VW + R S T b. A=T.U.V+X.Y+Y c. A=F. (E+F+G) d. A=(P.Q+R+ST)T.S e. A=D.DE f. A=Y.(W+X+Y+Z) - Z g. A = (B.E+C+F). C Construct the operation XOR from the basic Boolean operations AND, OR, and NOT. Given a NOR gate and NOT gates, draw a logic diagram that will perform the three- input AND function. Write the Boolean expression for a four-input NAND gate. 12.4 12.5 12.6 12.7