Math 2.0

definition

Disjunction

Definition

Let pp and qq be propositions. The disjunction of pp and qq is the proposition p∨qp \lor q, read "pp or qq". The proposition p∨qp \lor q is false when pp is false and qq is false. In all other cases, p∨qp \lor q is true.

pp qq p∨qp \lor q
T T T
T F T
F T T
F F F

Remarks

This "or" is inclusive: p∨qp \lor q is true when both pp and qq are true. The exclusive "or" is true when exactly one of pp and qq is true. The union of two sets uses disjunction: x∈A∪Bx \in A \cup B means x∈A∨x∈Bx \in A \lor x \in B.

Explanations

L1 human

The sentence "44 is even or 44 is odd" is a disjunction. It is true, because one part is true. In mathematics, "or" also allows both parts to be true.

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  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

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Proposition, concept, no evidence levelPropositionconceptDisjunction, definition, no evidence levelDisjunctiondefinition
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  1. Proposition concept
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Sources

  1. Web https://en.wikipedia.org/wiki/Logical_disjunction, lead section

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