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.