In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement)...

every element of ∅ {\displaystyle \varnothing } , the property P holds (vacuous truth). There is no element of ∅ {\displaystyle \varnothing } for which the...

true regardless of the truth value of the antecedent P if the consequent is fixed as true. A related concept is a vacuous truth, where the antecedent P...

In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative...

change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary...

fallacy Logical extreme Logical fallacies Reductio ad absurdum Straw man Vacuous truth K. S. Pope (2003). "Common Logical Fallacies in Psychology: 26 Types...

fulfilling a given predicate P(x) – exist in the empty set. See also Vacuous truth for more information. In category theory and the theory of elementary...

Quantum vacuum fluctuations Ultimate fate of the universe Vacuum Vanitas Vacuous truth Void (disambiguation) Zero Lincoln, Don (16 February 2023). ""Nothing"...

operators and symbols in Unicode Non-logical symbol Polish notation Truth function Truth table Wikipedia:WikiProject Logic/Standards for notation "Named character...

{\displaystyle M} is empty, the condition given above is an example of a vacuous truth. So the intersection of the empty family should be the universal set...