(Solved): The conditional operator of Propositional Logic, " ", is defined by the identity pqp ...

The conditional operator of Propositional Logic, " $?$ ", is defined by the identity $p?q?\neg p?q$ (a) Use (1.1) and identities from the list on the previous page to show algebraically that $[8\%]$ the compound proposition $((p?q)?p)?q$ is a tautology. State which identity you are using at each step, referring to it by number (e.g. A2). (b) The compound propositions $s$ and $t$ are defined in terms of three propositions $p,q$ and $r$ $[10\%]$ as follows: $\begin{array}{l}s=(p?q)?(q?r)?(r?p)\\ t=(p?q?r)?(\neg p?\neg q?\neg r)\end{array}$ Construct a truth table for $s$ and $t$, including columns for $p,q,r,p?q,q?r$, $r?p,p?q?r,\neg p?\neg q?\neg r,s$ and $t$. Hence show that $[2\%]$ $(p?q)?(q?r)?(r?p)?(p?q?r)?(\neg p?\neg q?\neg r)$