(a) draw up the i/o table for the boolean expression s = (r. 2)(y + 2). use column headings: x, y, 2, 2, y + 3,2 and finally sor (27)(y + 3). (b) use your answer to (a) to write down the dnf for s. (c) complete the following proof of the boolean algebra theorem, 1+2= 1, by filling in the missing properties used for each step. commutative and associative properties are used without actually noting they are being used. property used (i) 1+1 = (1 + 7) + = x+r+ = + the boolean algebra properties are listed near the end of lecture-workshop 3, and in the discrete mathematics text- book (pdf) on lms. 1 (d) write down the dual of the proof above, listing the axioms/properties used for each step.