Determine whether (¬p ∧ (p → q)) → ¬q is a tautology. 1 A statement that is a tautology is by definition a statement that is always true, and there are several approaches one could take to evaluate whether this is the case: (1) Truth Tables - For one, we may construct a truth table and evaluate whether every line in the table is in fact true This is fine when the statement is relatively short
What exactly does tautology mean? - Mathematics Stack Exchange To simplify, a tautology in plain English is stating the same thing twice but in a different manner So for example, the statement " this meaningless statement is non-meaningful " is a tautology, because it is essentially restating the same thing
I cant seem to prove that (p ∨ q) ∧ (¬p ∨ r) → (q ∨ r) is a tautology. I'm stuck on this last step The only law that seemed hopeful was the distribution law but that won't even work here I resorted to using a truth table to prove this but I really want to know if it's possible to shrink this proposition to just true to make it a tautology Thank you!
How to prove that $ [ (p→q)∧ (q→r)]→ (p→r)$ is a tautology without . . . 0 Another way to show a formula is a tautology is to derive the formula from an empty set of premises using the inference rules of your given system So, if you're working with a natural deduction system consisting of the inference rules Modus Ponens (MP), Conjunction Elimination ($\wedge$ E), and Conditional Proof (CP), then you can show