(Solved):   \[ p \wedge(q \vee r) . \] and then (ii) the truth table of the proposition \[ (p \wedge q ...

 

\[ p \wedge(q \vee r) . \] and then (ii) the truth table of the proposition \[ (p \wedge q) \vee(p \wedge r) . \] Here and below (in Problems 4, 5), all your truth tables must reflect the process of building a compound proposition under consideration frotn propositional variables (your solution(s) will be downgraded, otherwise). Say, the truth table for the compound proposition in (i) must be as follows: (iii) Compare the truth tables, and make a conclusion on the equivalence of the propositions, thereby proving that \[ p \wedge(q \vee r) \equiv(p \wedge q) \vee(p \wedge r) \] (if your truth tables are not identical, redo the problem). To present the answers to the problem, please include in your document both truth tables you've created in (i,ii), followed by the conclusion you've made in (iii).