Fortune Telling Collection - Fortune-telling birth date - What is the truth table of propositional formula?

What is the truth table of propositional formula?

The truth table of this propositional formula is as follows:

Its disjunctive formula: (﹁p→q)→(q→﹁p) is equivalent to a disjunctive formula.

This disjunction is either (﹁p→q) wrong or (q→﹁p) right.

That is, ﹁(﹁p→q)∨(q→﹁p) ﹁ (q → ﹁ p) ﹁.

Propositional formula, also known as compound formula, is a mathematical logic term and a symbol sequence formed according to certain laws.

Extended data:

Definition? Propositional formulas, also known as propositional formulas (formulas for short), can be generated according to the following rules:

The (1) propositional variable is a propositional formula.

(2) If A is a propositional formula, then? A is a propositional formula.

(3) If A and B are propositional formulas, then (A∧B), (A∨B), (A→B) and (A? B) They are all propositional formulas.

(4) If and only if (1), (2) and (3) are used in a limited way, the symbol string containing propositional variables, conjunctions and brackets is a propositional formula.

The definition of propositional formula is a recursive definition form. The propositional formula itself is not a proposition and has no truth value. Only after assigning a value to its propositional variable can it have a true value.

The five connection operators have different priorities. When they appear in a propositional formula at the same time, what is the operational priority between connections? 、∧、∨、→、? If there are parentheses, the operation in parentheses takes precedence.

Classification of propositional formulas

Tautology

Given a propositional formula, if the truth value of the propositional formula is always 1 for any set of propositional variables, then the propositional formula is called tautology or eternal truth.

Expression of contradiction

Given a propositional formula, if the true value of the propositional formula is always 0 for any group of propositional variables, it is said that the propositional formula is contradictory or always false.

Satisfiable formula

Given a propositional formula, if at least one set of assignments makes the true value of the formula 1, the propositional formula is said to be satisfiable.

By definition, formula? (P∧Q)? P∨? Q is eternal, formula? (P→Q)∧Q is a permanently false formula, and the true value of permanently true formula is always 1, so it is a special satisfiable formula.

Baidu Encyclopedia-Proposition Formula

Baidu encyclopedia-truth table