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In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...
Equivalents of the Axiom of Choice is a book in mathematics, collecting statements in mathematics that are true if and only if the axiom of choice holds. It was written by Herman Rubin and Jean E. Rubin, and published in 1963 by North-Holland as volume 34 of their Studies in Logic and the Foundations of Mathematics series.
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
Logical connectives can be used to link zero or more statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a unary connective, and so on.
Fiveable, an online learning community for high school students, made its first-ever acquisition earlier this week: Hours, a virtual study platform built by a 16-year-old. Fiveable is a free ...
is also equivalent over to the statement that every pruned tree with levels has a branch (proof below). Furthermore, D C {\displaystyle {\mathsf {DC}}} is equivalent to a weakened form of Zorn's lemma ; specifically D C {\displaystyle {\mathsf {DC}}} is equivalent to the statement that any partial order such that every well-ordered chain is ...
Plus, why these common statements may negatively impact your kids. Related: 12 Phrases Psychologists Are Begging Parents and Grandparents To Stop Saying to an Oldest Child Impacting a Child’s ...