(Solved): a. Using the laws and theorems of Boolean Algebra alone, prove the Consensus Theorem. Apply at mos ...

a. Using the laws and theorems of Boolean Algebra alone, prove the Consensus Theorem. Apply at most one law or theorem on each line and write down the name of the law or theorem that you used. Marks will be deducted if these instructions are not followed. (3 marks) b. Prove therefore that \( \left.\left(X^{\prime}+Y\right) .\left(X+Z^{\prime}\right) .\left(Y+Z^{\prime}\right)\right)=\left(X^{\prime}+Y\right) .\left(X+Z^{\prime}\right) \). Again, use at most one law or theorem on each line and name your law or theorem. Marks will be deducted if these are not done. (1 mark) c. Using the laws and theorems of Boolean Algebra alone, find the simplest SOP expression for this function. As before use at most one law or theorem on line and write down the name of the law or theorem that you used. (4 marks) \[ f(A, B, C, D)=\sum m(0,1,2,3,4,5,6,7,12,13,14,15) \]