Quiz 1
Discrete Mathematics · 1 problem · solutions hidden, click to reveal
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Problems
Consider the compound proposition \(((\neg p \lor q) \leftrightarrow r) \leftrightarrow r\).
(1) Construct a truth table for it.
(2) Find a compound proposition using only one connective (one of \(\neg, \lor, \land, \oplus, \to, \leftrightarrow\)) that has the same truth value for all \(p,q,r\). (Your answer should not involve \(r\).)
(1) Construct a truth table for it.
(2) Find a compound proposition using only one connective (one of \(\neg, \lor, \land, \oplus, \to, \leftrightarrow\)) that has the same truth value for all \(p,q,r\). (Your answer should not involve \(r\).)
Show solution
Answer: (2) \(p \to q\).
A biconditional with the same variable on both sides cancels: \((A \leftrightarrow r) \leftrightarrow r \equiv A\). Here \(A = \neg p \lor q\), so the whole proposition is equivalent to \(\neg p \lor q\), which is exactly \(p \to q\).