File:Venn1011.svg · Wikimedia Commons · See Wikimedia Commons
material implication
Sign in to saveAlso known as implication, material consequence, simply implication, implies, conditional, material conditional, if-then, logical implication
logical connective between two assertions, frequently symbolized by a (most often double) arrow to the right
Key facts
- Definition
- x → y {\displaystyle x\to y}
- Truth table
- ( 1011 ) {\displaystyle (1011)}
- Disjunctive
- x ¯ + y {\displaystyle {\overline {x}}+y}
- Conjunctive
- x ¯ + y {\displaystyle {\overline {x}}+y}
- Zhegalkin polynomial
- 1 ⊕ x ⊕ x y {\displaystyle 1\oplus x\oplus xy}
- 0 preserving
- no
- 1 preserving
- yes
- Monotone
- no
- Affine
- no
- Self dual
- no
via Wikipedia infobox
Wikidata facts
- Instance of
- Boolean function
- Subclass of
- proposition
- Image
- Venn1011.svg
Show 6 more facts
- maintained by WikiProject
- WikiProject Mathematics
- Unicode character
- ⟶
- different from
- material implication
- TeX string
- \longrightarrow
- studied by
- Boolean algebra
- Commons category
- Material conditional
Sources (3)
via Wikidata · CC0
~17 min read
Encyclopedic overview
Related concepts
Propositional calculus Predicate logic Boolean algebra Truth table Truth function Boolean function Functional completeness Scope (logic)
Excerpted from Wikipedia’s “material implication” article, available under the CC BY-SA 4.0 licence.