Theorems in propositional logic | Rules of inference

Biconditional introduction

In propositional logic, biconditional introduction is a valid rule of inference. It allows for one to infer a biconditional from two conditional statements. The rule makes it possible to introduce a biconditional statement into a logical proof. If is true, and if is true, then one may infer that is true. For example, from the statements "if I'm breathing, then I'm alive" and "if I'm alive, then I'm breathing", it can be inferred that "I'm breathing if and only if I'm alive". Biconditional introduction is the converse of biconditional elimination. The rule can be stated formally as: where the rule is that wherever instances of "" and "" appear on lines of a proof, "" can validly be placed on a subsequent line. (Wikipedia).

Video thumbnail

Bipartite II - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

Bipartite III - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

Bipartite I - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

Natural Deductive Logic: RULES #3 (=I, =E) - Logic

In this video on #Logic, we learn our last two rules for natural deductive proofs. We learn biconditional introduction and biconditional elimination. Then we do a few example proofs. #PropositionalLogic #LogicProofs 0:00 [Rule: Biconditional Introduction] 1:47 [Rule: Biconditional Elimin

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Solve a multi step equation with variables on the same side ex 15, 4(3y–1)–5y=–11

👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes

From playlist How to Solve Multi Step Equations with Parenthesis

Video thumbnail

Solve a multi step equation with two variables and distributive property ex 19, –7=3(t–5)–t

👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes

From playlist How to Solve Multi Step Equations with Parenthesis

Video thumbnail

TRUTH TREES with Negation, Conditional, and Biconditional - Logic

In this video on #Logic / #PhilosphicalLogic I introduce rules for the conditional and biconditional for truth trees. We talk about conditional decomposition, biconditional decomposition, negated conditional decomposition, and negated biconditional decomposition. Then, we do an example of

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Two exercises in TRUTH TREES with Negation, Conditional, and Biconditional - Logic

We do two exercises in truth trees with conditionals and biconditionals. 0:00 [Intro] 0:19 [Question #1] 3:14 [Question #2] Follow along in the Logic playlist: https://www.youtube.com/playlist?list=PLDDGPdw7e6AhsNuxXP3D-45Is96L8sdSG If you want to support the channel, hit the "JOIN" but

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Two practice exercises in Natural Deductive Logic: RULES #3 (=I, =E) - Logic

We do two practice exercises on natural deductive proofs using biconditional elimination, biconditional introduction, and all of our rules from before. These proofs are quite long, between 15 and 25 lines each! #PropositionalLogic #LogicProofs 0:00 [Intro] 0:20 [Question #1] 9:02 [Questi

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Deductive Reasoning If Then Statements

I introduce deductive reasoning by introducing the structure of "if, then" statements. I explain conditional statements, converse statements, bi-conditional statements, inverse statements, and finally contrapositive statements. Find free review test, useful notes and more at http://www.ma

From playlist Geometry

Video thumbnail

How to TRANSLATE ENGLISH into PROPOSITIONAL LOGIC - LOGIC

In this video on #Logic / #PhilosophicalLogic we learn how to translate English into propositional logic. We learn the five basic operators, "not", "and", "or", "if then", and "if and only if", also known as the negation, the conjunction, the disjunction, the conditional, and the biconditi

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Solving a multi step equation

👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes

From playlist How to Solve Multi Step Equations with Parenthesis

Video thumbnail

Solving a multi step equation using distributive property

👉 Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To

From playlist How to Solve Multi Step Equations with Parenthesis on Both Sides

Video thumbnail

SYNTAX of PROPOSITIONAL LOGIC and WELL-FORMED FORMULAS (wffs) - LOGIC

In this video on #Logic / #PhilosophicalLogic we take a look at the requirements of well-formed formulas (wffs) in propositional logic and how to draw syntactic trees for wffs. Then we do some practice questions. 0:00 [Intro] 0:16 [Syntax of PL] 2:10 [Wffs] 4:36 [Example of a Wff #1] 6:56

From playlist Logic in Philosophy and Mathematics

Video thumbnail

How to solve a multi step equation with a variable on both sides

👉 Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To

From playlist How to Solve Multi Step Equations with Parenthesis on Both Sides

Video thumbnail

Learn how to solve a linear equation by applying the distributive property of negative 1

👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes

From playlist How to Solve Multi Step Equations with Parenthesis

Video thumbnail

Logic - Biconditional

An introduction to a biconditional or if and only if statement

From playlist Geometry

Video thumbnail

How to draw TRUTH TABLES in PROPOSITIONAL LOGIC

In this video we look at truth tables in #Logic / #PhilosophicalLogic propositional logic for negation, the conjunction, the disjunction, the conditional, and the biconditional. Then I give you an exercise to look at the Quine Dagger. We also do some practice! 0:00 [Intro] 0:20 [What is a

From playlist Logic in Philosophy and Mathematics

Video thumbnail

Applying distributive property with a negative one to solve the multi step equation

👉 Learn how to solve multi-step equations with parenthesis. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-step equation with parenthes

From playlist How to Solve Multi Step Equations with Parenthesis

Video thumbnail

5. Ch. 2, Sections 2.2 & 2.3. Introduction to Logic, Philosophy 10, UC San Diego - BSLIF

Video lecture corresponding to _Basic Sentential Logic and Informal Fallacies_, Chapter 2, Sections 2.2 & 2.3. This is for the class Introduction to Logic, Philosophy 10, UC San Diego.

From playlist UC San Diego: PHIL 10 - Introduction to Logic | CosmoLearning.org Philosophy

Related pages

Tautology (logic) | Validity (logic) | Propositional calculus | Converse (logic) | Logical consequence | Biconditional elimination | If and only if | Metalogic | Rule of inference | Formal system | Inference | Sequent | Theorem | Material conditional | Formal proof | Logical biconditional