0.2 Logical connectives

Negation: ¬p 

The negation ¬p ('not p') of a proposition p is the proposition which is TRUE if p is FALSE, and FALSE if p is TRUE.

  p  |  ¬p

  T  |   F

  F  |   T

 

Disjunction (union): p ∨ q

The union p ∨ q ('p or q') of two propositions p, q is the proposition which is TRUE if at least one of the propositions p, q is TRUE, and FALSE otherwise.

  p  |  q  |  p∨q

  T  |  T  |   T

  T  |  F  |   T

  F  |  T  |   T

  F  |  F  |   F

 

Conjunction (intersection): p ∧ q

The intersection p ∧ q ('p and q') of two propositions p, q is the proposition which is TRUE if both the propositions p, q are TRUE, and FALSE otherwise.

  p  |  q  |  p∧q

  T  |  T  |   T

  T  |  F  |   F

  F  |  T  |   F

  F  |  F  |   F

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