<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Invalid Arguments · Maximum Mathematics</title><link>https://maximummathematics.com/books/foundational-mathematics/proof/invalid-arguments/index.html</link><description>All of us have, at one point, been presented with an argument that doesn’t seem quite right. Just because someone can string together a group of premises and assert some conclusion doesn’t mean that conclusion actually follows from the premises.
Remember that an argument is valid if the argument’s implication is a logical implication — meaning that no matter what truth values the argument’s propositions have, the overall implication always evaluates to $1$. This means that if we can come up with even one truth value assignment reducing to the form $1 \to 0$, the argument isn’t valid. In other words, for any argument $(p_1 \land p_2 \land \dots \land p_n) \to c$ with $c = 0$ (and all premises true), the argument is invalid.</description><generator>Hugo</generator><language>en-US</language><atom:link href="https://maximummathematics.com/books/foundational-mathematics/proof/invalid-arguments/index.xml" rel="self" type="application/rss+xml"/></channel></rss>