6. Homework 01 Note: In the expressions"." represents (AND), "+" represents (OR) and "(single quote) represents (NOT the previous symbol). 1-) Use algebraic manipulation to prove that: x+y.z-(x + y). (x + 2) Note that this is the distributive rule. 2-) Use algebraic manipulation to prove that: (x + y). (x + y) = x 3-) Determine whether or not the following expressions are valid, i.e, whether the left and right- hand sides represent the same function: Show the reasoning, using truth table. 1-) x1'.x3 + x1.x2.x3" + xlx2 + x1.x2' = x2.x3 + x1.x3 + x2.x3 + xl'.x2.x3 b-)x1.x3 + x2.x3 + x2'.x3 = (x1 + x2 + x3). (x1 + x2 + x3). (xl' + x2 + x3) C-)(x1 + x3). (xl' + x2 + x3"). (xl' + x2) = (x1 + x2). (x2 + x3). (xl' + x3) 4-) Draw a timing diagram for the circuit in the Figure below. Show the waveforms that can be observed on all wires in the circuit. (show the output for all eight possible different input combination is sequence, from 000 up to 111 with one time tick for each state) SA x2 Us f x3 M x 1