Chapter 1: Propositional Logic

describe which conclusions one can draw from the structure of sentences and arguments without having to understand the content itself

formalization of the concepts of logic, which were then used as a basis for mathematics

can be used to model and solve practical problems on an abstract level

studies the truth values of propositions

assessing how the truth of one proposition relates to the truth of another.

first-order logic.

nature of the conclusions that can be drawn in such situations (i.e., when propositions contain variables that must be interpreted

statement that can be assigned a truth value. In other words, it can be assessed as true or false, an assessment that can be evaluated in terms of its adherence to reality.

statement that either is a single propositional variable or is built from multiple propositional variables that are connected to Boolean operators (also known as logical connectives).

NOT - Operator denotes as ¬

AND - Logical Injunction denoted as ∧

OR - Logical Disjunction denoted as ∨

IF-THEN - Implication denoted as ⇒

IF-AND-ONLY-IF - Equvalence as ⇔

XOR - denoted as ⊕

denoted as ⇒

proposition A ⇒ B is true unless A is true and B is false. If A is false, then the truth value of B does not matter, and the implication will always be evaluated as true

A ⇒ B can also be written as ¬A ∨ B

A ⇒ B Is disctinct from B ⇒ A

Denoted as ⇔

A ⇔ B evaluates to true if A and B have the same truth value.

A set B of Boolean operators is a complete basis if every other Boolean operator can be expressed with elements of B.

• OR and NOT form a complete basis.

• NAND forms a complete basis.

A literal is an expression that is either a single propositional variable (such as A) or a negated variable (such as NOT A). If a literal does not contain a negation, it is also called a positive literal. If it contains a negation, it is called a negative literal.