Chapter 1 - Section 1.1 - Propositional Logic - Exercises - Page 15: 36

See step by step work for the solution

a) $(p \lor q )\lor r$ \begin{array}{c|c|c|c|c|c|c |c} p & q & r & p \lor q & (p \lor q) \lor r \\ T & T & T & T& T \\ T & T & F & T& T\\ T & F & T & T& T\\ T & F & F & T& T \\ F & T & T & T& T\\ F & T & F & T& T\\ F & F & T & F& T\\ F & F & F & F& F \end{array} b) $(p \lor q )\land r$ \begin{array}{c|c|c|c|c|c|c |c} p & q & r & p \lor q & (p \lor q) \land r \\ T & T & T & T& T \\ T & T & F & T& F\\ T & F & T & T& T\\ T & F & F & T& F \\ F & T & T & T& T\\ F & T & F & T& F\\ F & F & T & F& F\\ F & F & F & F& F \end{array} c)$(p \land q )\lor r$ \begin{array}{c|c|c|c|c|c|c |c} p & q & r & p \land q & (p \land q) \lor r \\ T & T & T & T& T \\ T & T & F & T& T\\ T & F & T & F& T\\ T & F & F & F& F \\ F & T & T & F& T\\ F & T & F & F& F\\ F & F & T & F& T\\ F & F & F & F& F \end{array} d)$(p \land q )\land r$ \begin{array}{c|c|c|c|c|c|c |c} p & q & r & p \land q & (p \land q) \land r \\ T & T & T & T& T \\ T & T & F & T& F\\ T & F & T & F& F\\ T & F & F & F& F \\ F & T & T & F& F\\ F & T & F & F& F\\ F & F & T & F& F\\ F & F & F & F& F \end{array} e)$(p \lor q )\land \neg r$ \begin{array}{c|c|c|c|c|c|c |c} p & q & r & p \lor q &\neg r& (p \lor q) \land r \\ T & T & T & T& F& F \\ T & T & F & T& T&T\\ T & F & T & T& F&F\\ T & F & F & T& T&T \\ F & T & T & T& F&F\\ F & T & F & T& T&T\\ F & F & T & F& F&F\\ F & F & F & F& T&F \end{array} f)$(p \land q )\lor \neg r$ \begin{array}{c|c|c|c|c|c|c |c} p & q & r & p \land q&\neg r & (p \land q) \lor \neg r \\ T & T & T & T& F&T \\ T & T & F & T& T&T\\ T & F & T & F& F&F\\ T & F & F & F& T& T\\ F & T & T & F& F&F\\ F & T & F & F& T& T\\ F & F & T & F& F&F\\ F & F & F & F& T&T \end{array}