Discrete Mathematics · Propositional and predicate logic with proof methods

Let p, q, and r be propositions

Problem

Let \(p\), \(q\), and \(r\) be propositions. Using a complete truth table, determine whether \((p \to q) \land (q \to r)\) is logically equivalent to \(p \to r\). If the two formulas are not equivalent, exhibit a specific truth assignment that distinguishes them.

Hint

Equivalence of two formulas means they have the same truth value on *every* row of the table, not merely that one of them implies the other.

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