Ad
related to: definition of logically equivalent sentences worksheets pdfteacherspayteachers.com has been visited by 100K+ users in the past month
Search results
Results from the WOW.Com Content Network
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 ...
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants.
For example, the sentence "'Snow is white' is true" becomes materially equivalent with the sentence "snow is white", i.e. 'snow is white' is true if and only if snow is white. Said again, a sentence of the form "A" is true if and only if A is true. The truth of more complex sentences is defined in terms of the components of the sentence:
Such a logical connective as converse implication "" is actually the same as material conditional with swapped arguments; thus, the symbol for converse implication is redundant. In some logical calculi (notably, in classical logic), certain essentially different compound statements are logically equivalent.
Import-export expresses a deductive argument form.In natural language terms, the formula states that the following English sentences are logically equivalent: [1] [2] [3]. If Mary isn't at home, then if Sally isn't at home, then the house is empty.
logically equivalent Referring to statements that have the same truth value in every possible scenario, indicating that they are interchangeable in logical reasoning. logicism The philosophical belief that mathematics can be reduced to logic and that all mathematical truths can be derived from logical axioms and definitions. Löwenheim–Skolem ...
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
Ad
related to: definition of logically equivalent sentences worksheets pdfteacherspayteachers.com has been visited by 100K+ users in the past month