Formal Logic 1.1

A sentence that is either True or False.

Capital letters near the beginning of the alphabet, such as A, B, and C used to represent statements.

• Symbols used to represent and, or, then, if and only if...
• Used to connect statements.

The statement "A and B" expressed in symbolic form.

The statements "A" and "B" in a conjunction.

The statement "A or B" expressed in symbolic form.

The statements "A" or "B" in a disjunction.

• A statement in the form "If statement A, then statement B."
• Expressed in symbolic form, read as "A implies B."
• Conveys meaning, "The truth of A implies or leads to the truth of B."

In an implication, "A implies B," statement A.

In an implication, "A implies B," statement B.

• The statement expressed symbolically as, "(A implies B) AND (B implies A)."
• Also "if and only if"

Connectives that join 2 or more expressions together to produce a 3rd expression.

A connective acting on 1 expression to produce a 2nd expression, such as a negation.

A unary connective for "not" in symbolic form.

An expression that is a legitimate string, following correct syntax rules.

In a well-formed formula (wff) with a number of connectives, the connective to be applied last, following the order of precedence.

A well-formed formula (wff) whose truth values are always True; it is True no matter what truth values are assigned to its statement letters.

A well-formed formula (wff) whose truth values are always False; it is False no matter what truth values are assigned to its statement letters.

Such as what happens in a wff that is also a tautology as in "P if and only if Q."

A set of instructions that can be mechanically executed in a finite amount of time in order to solve some problem.

Algorithms written in natural language description that leave out the technical syntax of any given computer language.