In plain language, this means that if A is true, then B must be true and if A is false, then B must be false. Additionally, the third column contains an informal definition, the fourth column gives a short example, the fifth and sixth give the Unicode location and name for use in HTML documents. This means two things: "If P, Then Q" and "If Q, Then P". The English language is tremendously confusing compared to the simplicity of formal logic. One could take an umbrella on a walk even though it may not be raining outside. Thus the statement “P if and only if Q” becomes “P iff Q.”. In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, 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. 6 “Athena is a cat only if she is a mammal.” Gets translated as: A Ɔ M Note that “Athena is a cat only if she is a mammal” does NOT mean the same thing as “Athena is a cat if she is a mammal” since lots of mammals are not cats (for instance, Athena might be a dog). Produce the truth tables for the two conditional statements and use those to convince yourself that this logical equivalence holds. For a short if and only if, use \Leftrightarrow: A $\Leftrightarrow$ B. Then 6j(a b), so 6x = (a b) for some x 2Z. News; if and only if. Consider the statement “if today is Easter, then tomorrow is Monday.” Today being Easter is sufficient for tomorrow to be Monday, however, it is not necessary. 1965 June 4, John W. Tukey, Data Analysis and the Frontiers of Geophysics, in Science New Series, 148(3675), page 1288, In most logical systems, one proves a statement of the form "P iff Q" by proving either "if P, then Q" and "if Q, then P", or "if P, then Q" and "if not-P, then not-Q". Proof: Part 1: P )Q. An "if and only if" statement is also called a necessary and sufficient condition. Today could be any Sunday other than Easter, and tomorrow would still be Monday. More general usage. – RegDwigнt ♦ Dec 6 '13 at 13:41. [17] However, this logically correct usage of "if and only if" is relatively uncommon, as the majority of textbooks, research papers and articles (including English Wikipedia articles) follow the special convention to interpret "if" as "if and only if", whenever a mathematical definition is involved (as in "a topological space is compact if every open cover has a finite subcover").[18]. In fact, when "P if and only Q" is true, P can subsitute for Q and Q can subsitute for P in other compound … A quick guide to conditional logic. On the other hand, all cats ARE mammals. The brackets may be omitted after an if statement. Up Next. For example, P if and only if Q means that 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. The phrase “if and only if” is used commonly enough in mathematical writing that it has its own abbreviation. How to Do Hypothesis Tests With the Z.TEST Function in Excel, Example of Two Sample T Test and Confidence Interval, Differences Between Population and Sample Standard Deviations, How to Calculate a Sample Standard Deviation, Definition and Examples of Valid Arguments, Calculating a Confidence Interval for a Mean, Degrees of Freedom in Statistics and Mathematics, converse, inverse, and the contrapositive, B.A., Mathematics, Physics, and Chemistry, Anderson University. Another way to say the same things is: "Q is necessary, and sufficient for P". If you find our videos helpful you can support us by buying something from amazon. [3] Some authors regard "iff" as unsuitable in formal writing;[4] others consider it a "borderline case" and tolerate its use.[5].

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