symmetric implications

[/sɪˈmetrɪk ˌɪmpləˈkeɪʃənz/]
noun
implicações simétricas
1. A logical or mathematical relationship where two propositions or conditions mutually imply each other; if A implies B, then B also implies A (A ↔ B)
In mathematics, the symmetric implications between congruent triangles mean that if triangle ABC is congruent to triangle DEF, then triangle DEF is congruent to triangle ABC.
Em matemática, as implicações simétricas entre triângulos congruentes significam que se o triângulo ABC é congruente ao triângulo DEF, então o triângulo DEF é congruente ao triângulo ABC.
2. A logical principle where the truth of a biconditional statement ensures that both directions of implication hold equally
The symmetric implications of the theorem allow us to use it in either direction without loss of generality.
As implicações simétricas do teorema nos permitem usá-lo em qualquer direção sem perda de generalidade.
This is primarily a technical term used in mathematics, logic, and formal reasoning contexts. It is employed equally in both Brazilian Portuguese and European Portuguese academic settings. The concept is fundamental to higher mathematics and formal logic courses in both English and Portuguese-speaking countries.
Synonyms / Sinônimos
biconditional implicationsmutual implicationsequivalence relationstwo-way implications
Antonyms / Antônimos
asymmetric implicationsone-way implicationsunidirectional implications

Regional Variations

General Brazilian
implicações simétricas
Standard usage in mathematics and logic
Portugal
implicações simétricas
Same as Brazilian Portuguese; academic and technical context
Academic English
implicações bidirecionais
Alternative translation emphasizing the two-way nature

Related Words

logical implicationbiconditionalequivalencecongruencemutual implicationlogical equivalence

Related Idioms & Phrases

goes both ways
cut both ways
works in either direction
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