Logical connectives | Necessity and sufficiency | Mathematical terminology
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, P if and only if Q means that P is true whenever Q is true, and the only case in which P is true is if Q is also true, whereas in the case of P if Q, there could be other scenarios where P is true and Q is false. In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. Some authors regard "iff" as unsuitable in formal writing; others consider it a "borderline case" and tolerate its use. In logical formulae, logical symbols, such as and , are used instead of these phrases; see below. (Wikipedia).
This lesson defines the meaning of an if and only if statement.
From playlist Mathematical Statements (Discrete Math)
Mathsplanations: What does "iff" mean?
We discuss the idea of necessary and sufficient conditions using easy-to-grasp examples. Another useful dose of Maths for everyone by Dr Sarada Herke. For more Math-y goodness check out my Graph Theory channel http://youtube.com/drsaradaherke
From playlist Mathsplanations
Biconditional Statements | "if and only if"
A biconditional statement is one of the form "if and only if", sometimes written as "iff". The statement "p if and only if q" means "p implies q" AND "q implies p". That is, it is a conjunction of two individual conditional statements. In this video we will see how to write and interpret s
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
If-Then Statements and Converses
http://mathispower4u.wordpress.com/
From playlist Logic (If-Then Statements, Truth Tables)
Mathsplanations: If-Then Statements and Lying
The truth table for an If-Then statement is easy to remember if you just keep track of when you've been lied to. Here we'll explore it with a simple example. Another useful dose of Maths for everyone by Dr Sarada Herke. For more Math-y stuff, check out my other channel http://youtube.com/
From playlist Mathsplanations
Truth Table for the Biconditional Statement
http://mathispower4u.wordpress.com/
From playlist Logic (If-Then Statements, Truth Tables)
The Converse, Contrapositive, and Inverse of an If-Then Statement
http://mathispower4u.wordpress.com/
From playlist Logic (If-Then Statements, Truth Tables)
Determining the truth of a conditional statement
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
How to determine the truth table from a statement and determine its validity
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
Juan José Nuño-Ballesteros: Equisingularity of map germs from a surface to the plane
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
NOT ONLY will you have excellent grammar but you'll look cool too: Using INVERSION
How to use NOT ONLY....BUT ALSO in English. An advanced English grammar lesson to show surprise when talking about two things. We use "inversion" to really emphasise the phrase everything is explained in this lesson by LetThemTalkTV Intermediate and advanced English lessons with subtitle
From playlist Use the right word - Useful English vocabulary
Crud Operations In MongoDB | MongoDB CRUD Operations With Examples | MongoDB Training | Edureka
(** MongoDB Certification Training - https://www.edureka.co/mongodb **) This Edureka CRUD Application in MongoDB video covers in-depth knowledge about how to perform Create, Read, Update & Delete operations in MongoDB. The topics covered in this video are: Creating Database Creating Colle
From playlist MongoDB Dev & Admin Tutorial Videos
Math Explorations Ep22, Euler circuits & paths (Mar 23, 2022)
This is a recording of a live class for Math 1015, Mathematics: An Exploration, an undergraduate course for non-technical majors at Fairfield University, Spring 2022. The major topics are voting, gerrymandering, and graph theory. Handouts and homework are at the class website. Class web
From playlist Math 1015 (Mathematical Explorations) Spring 2022
3/2 Firefighters Are Not Enough - Rani Hod
Rani Hod Tel Aviv University November 2, 2010 The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic. In more detail, a fire spreads through a graph, from burning vertices
From playlist Mathematics
Lecture 13: Spanner MIT 6.824: Distributed Systems (Spring 2020) https://pdos.csail.mit.edu/6.824/
From playlist MIT 6.824 Distributed Systems (Spring 2020)
Piers Cawley OSCON 2014 Keynote: "Something to Remember"
From OSCON 2014: Keynote by Piers Cawley, Perl programmer, singer and balloon modeller. About Piers Cawley (Thermeon): Piers Cawley started programming Perl in the mid nineties, but recently spent a few years working as a Ruby programmer. He's currently writing Perl for Thermeon Europe
From playlist OSCON 2014
logical equivalences -- proof writing examples 4
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.
From playlist Proof Writing
CCSS What are truth tables and how can we create them for conditional statements
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
Polynomial chaos and scaling limits of disordered systems - Nikolaos Zygouras
Nikolaos Zygouras University of Warwick December 3, 2013 Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting
From playlist Mathematics