Question

Show that ( p → q) ∧ ( q → r) → ( p→ r) is a tautology by using truth table or rules of

logical equivalence

Answer 1

$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c:c} p & q & r & p\rightarrow q & q\rightarrow r & (p\rightarrow q)\land (q\rightarrow r) & p\rightarrow r& (p\rightarrow q)\land (q\rightarrow r) \rightarrow ( p\rightarrow r) \\ \hline T & T & T &T&T&T&T&T \\ \hdashline T & T & F&T&F&F&F&T \\ \hdashline T&F&T&F&T&F&T&T \\ \hdashline F&T&T&T&T&T&T&T \\ \hdashline T&F&F&F&T&F&F&T \\ \hdashline F&T&F&T&F&F&T&T \\ \hdashline F&F&T&T&T&T&T&T \\ \hdashline F&F&F&T&T&T&T&T \end{array}$