1. Consider the Boolean function (a) Obtain the truth table of the Boolean function. (b) Simplify the Boolean function using the theorems and identities. (c) Simplify the Boolean function using K-map. (d) Implement the simplified function using NAND gates only FX,YZ)-? (13.7). 2. Implement a full adder using two 4-to-1 multiplexers. Prove the following theorem: (a) Using K-map. (b) Using Boolean algebra. 3. XY + X' Z + YZ = XY + XZ 4. Implement the following four Boolean expressions using three half adders E = A, B C + AB, C F = ABC, + (A' +B') C GABC