3. Simplification of Boolean Expression using Boolean Algebra F(A,B,C) AB + BC + ABC (a) Given the expressions F above, simplify the expression using Boolean Algebra and show the simplified equation. Show each step of the simplification clearly. (b) Create appropriate circuits using Cedar Logic and truth tables to show that the original expression and the simplified expression are equivalent. (c) Implement the Sum-of-Product boolean expression AB + CD using only NOR gates. Ensure that the number of NOR gates used in the circuit is the minimum needed. (d) Implement the Product-of-Sum boolean expression (A + B)(C+ D)CD using only NAND gates. Ensure that the number of NAND gates used in the circuit is the minimum needed.