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The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows 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- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
Definition Truth table Logic gate ... The material conditional (also known as material implication) is an operation commonly used in logic. ... When disjunction, ...
Related puzzles involving disjunction include free choice inferences, Hurford's Constraint, and the contribution of disjunction in alternative questions. Other apparent discrepancies between natural language and classical logic include the paradoxes of material implication , donkey anaphora and the problem of counterfactual conditionals .
It is the negation of material implication. That is to say that for any two propositions P {\displaystyle P} and Q {\displaystyle Q} , the material nonimplication from P {\displaystyle P} to Q {\displaystyle Q} is true if and only if the negation of the material implication from P {\displaystyle P} to Q {\displaystyle Q} is true.
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
14, OR, Logical disjunction; 15, true, Tautology. Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
Some of these connectives may be defined in terms of others: for instance, implication, p → q, may be defined in terms of disjunction and negation, as ¬p ∨ q; [74] and disjunction may be defined in terms of negation and conjunction, as ¬(¬p ∧ ¬q). [51]