MATH 301, DISCRETE MATHEMATICS FALL 2022-HOMEWORK II DUE 11.59PM CT TUESDAY, 13TH SEPTEMBER (1) For t > 0, let Ct = {(x, y) E R2 | max(|x], ly)) = t} Is C = {Ct | t E [0, co) } a partition of R x R? Show your work. (2) Show that both P1 = {S, : {r} x R}rER and P2 = {As = RX {s} }SER are partitions of R2 = R X R. Also draw a rough picture of how both the collection looks like. (3) Construct a truth table for the following statement forms, and from which determine if they logically equivalent or not. (~pAq) Vr and ~ p/ (q Vr)