Like OP, I think that a truth table is not even applicable for if-then. Here's why: Let's say P = "The earth is flat" and Q = "I'm 24 years old". We know that P is false. I happen to be 24 years old. So, according to the truth table, the fact that the earth is flat somehow implies that I'm 24 years old. This sounds ridiculous. $\endgroup$ –

Sep 19, 2021 · What this truth table represents is the fact that if you have a data set (or situations) that results in a false value of (~A V B) then your assumption that A implies B is violated (or is not correct). In simpler words, the true values in the truth table are for the statement A implies B.

Sep 20, 2018 · Said differently, since the truth-value of a material implication is a function of the truth-values of its antecedent and consequent alone, then we will look only to the truth-values, not to the content, of the antecedent and consequent. This is consistent with the aim of disregarding content and representing only the logical form of statements ...

Dec 13, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Aug 10, 2023 · Q2: I've never seen that statement presented as an axiom, I'd imagine it's usually presented as a tautology or Identity. Q3: Your approach is a bit misguided,p → q is a convenient shorthand for the statement: ¬ p ∨ q Once we have defined ¬ and ∨, then the truth table for → follows from that. $\endgroup$ –

Mar 25, 2017 · Since an argument is valid if and only if it is impossible for the premises true and the conclusion false, we are interested in exactly the presence or absence of such a row in the full truth-table: if there is a row where the premises are true and the conclusion is false then the argument is invalid, but if there is no such row, then it is valid.

$\begingroup$ mistakes in table 3: first row - don't forget that in if..then.. claim (a=>b), when the a part is false, the entire claim is true. last row - when ~q and ~p are true, the claim ~q=>~p is true, it applies directly. when fixing that, your table matches mine. $\endgroup$

Aug 7, 2021 · After practicing filling truth table and gaining logic terminologies, the natural language intuition for "if p then q" is generally that p is a sufficient condition of q, while for "p only if q" q is a necessary condition for p. With these intuitions you …

Dec 18, 2016 · I will also point out that the truth table in the original post is not complete. You have to put a T or F under each logical operator and each atomic statement in your table. Each box therefore requires 2 truth values in this example. One for the main logical operator and one for the atomic statement(in parentheses).

Sep 12, 2020 · $\begingroup$ Do you agree that such answer only justifies what the truth table is rather than explaining why is it the way it is? To be more clear, why do we need if $19<4$ then $19<6$ to be a true statement? What if we consider it a false statement does it make any problem? $\endgroup$ –