Propositional Logic Worksheet Page 21
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21Equivalence Proofs using the Logical Identities
Example - our first step by step equivalence proof
Show P ∧ ¬Q ≡ ¬(P → Q). Hint: You will need to use the fact
that P → Q ≡ ¬P ∨ Q (we just proved this).
Example: Show that (P ∧ Q) → P is a tautology.
Note: We can also use a truth table to prove a compound proposi-
tion is a tautology, but this is only practical if the number of propo-
sitional variables is small.
Exercise: Show ¬P → (P → Q) is a tautology, first using a truth
table and then with an equivalence proof.
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