Appropriate for questions about truth tables, conjunctive and disjunctive normal forms, negation, and implication of unquantified propositions. Also for general questions about the propositional calculus itself, including its semantics and proof theory. Questions about other kinds of logic should use a different tag, such as (logic), (predicate-logic), or (first-order-logic).
Propositional logic is a branch of logic dealing with logical connectives and statements involving them. A logical connective connects finitely many sentences and forms a compound sentence, in a way that the truth value of the compound sentence depends only on the truth value of its constituents. The most common connectives are the binary connectives conjunction ($\land$), disjunction ($\lor$) and implication ($\rightarrow$), the unary connective negation ($\neg$), and the nullary connectives true ($\top$) and false ($\bot$).
Any proposition is considered to be either atomic (in which case it has no constituents) or compound (in which case it's formed by mean a connective using simpler propositions). A propositional model is a function assigning to each atomic proposition a truth value $0$ or $1$. The truth values of compound propositions are then determined by the truth values of their constituents. For example, if $I$ is a function assigning truth values to propositions, one would have $I(\top)=1$, $I(\bot)=0$, $I(\neg A)=1-I(A)$, $I(A\land B)=\min\big(I(A),I(B)\big)$, $I(A\lor B)=\max\big(I(A),I(B)\big)$ and $I(A\rightarrow B)=\max\big(1-I(A),I(B)\big)$. The propositions having the value $1$ for every model, are called tautologies, and those having the value $0$ for every model, are called absurdities. A central task of propositional logic is characterizing tautologies and absurdities.
