Why was the horseshoe symbol (⊃) selected for Material Implication?


What does the horseshoe symbolize in logic?

The horseshoe symbol is used to translate a conditional statement. The biconditional is a compound statement made up of two conditionals: one indicated by the word “if” and the other indicated by the phrase “only if.”

What does ⊃ mean?

Horseshoe (⊃, \supset in TeX) is a symbol used to represent: Material conditional in propositional logic. Superset in set theory.

What does ⊃ mean in logic?

material implication

The ⊃ symbol is used to symbolize a relationship called material implication; a compound statement formed with this connective is true unless the component on the left (the antecedent) is true and the component on the right (the consequent) is false, as shown in the truth-table at the right.

What is the symbol for implication?

Basic logic symbols

Symbol Unicode value (hexadecimal) Logic Name
U+21D2 U+2192 U+2283 material implication
⇔ ≡ ⟷ U+21D4 U+2261 U+27F7 material equivalence
¬ ˜ ! U+00AC U+02DC U+0021 negation
U+1D53B Domain of discourse

What is the name of this symbol ⊃ in a set?

Mathematics Set Theory Symbols

Symbol Symbol Name Example
A ⊂ B proper subset / strict subset {7, 13, 15} ⊂ {1, 7, 9, 13, 15, 23}
A ⊃ B proper superset / strict superset {1, 7, 9, 13, 15, 23} ⊃ {7, 13, 15, }
A ⊇ B superset {1, 7, 9, 13, 15, 23} ⊃ {7, 13, 15, 21}
Ø empty set C = {Ø}
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What is material implication philosophy?

In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and that either form can replace the other in logical proofs.

What is an implication and how it is derived?

noun. something implied or suggested as naturally to be inferred or understood: to resent an implication of dishonesty. the act of implying: His implication of immediate changes surprised us. the state of being implied: to know only by implication.

What do you mean implication?

: something that is suggested without being said directly : something that is implied. [count] I’m offended by his implication that women can’t be good at mathematics. I resent that/your implication!

What is this symbol called?

This table contains special characters.

Symbol Name of the symbol Similar glyphs or concepts
‘ ‘ Apostrophe Quotation mark, Guillemet, Prime, Grave
* Asterisk Asterism, Dagger
Asterism Dinkus, Therefore sign
@ At sign

What does * * mean?

a small starlike symbol (*), used in writing and printing as a reference mark or to indicate omission, doubtful matter, etc. Linguistics. the figure of a star (*) used to mark an utterance that would be considered ungrammatical or otherwise unacceptable by native speakers of a language, as in * I enjoy to ski.

What logical operator is denoted by the symbol ⋀?

Generalized Logical Connectives

Symbol Name Explanation Example
⋀ i = m n P i Generalized conjunction ( P m ∧ ⋯ ∧ P n ) ⋀ i = 1 n [ i ≠ ( i + 1 ) ]
⋁ i = m n P i Generalized disjunction ( P m ∨ ⋯ ∨ P n ) ¬ ( ⋁ i = 1 n P i ) = ⋀ i = 1 n ¬ P i
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