Mathematics for Computer Science MIT 6.042J/18.062J

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Presentation transcript:

Mathematics for Computer Science MIT 6.042J/18.062J Predicates & Proof

Propositions with variables Predicates Predicates are Propositions with variables Example:

Predicates For x = 1 and y = 3, is true For x = 1 and y = 4, is false is true

Quantifiers For ALL x There EXISTS some y

Quantifiers x, y range over Domain of Discourse True over Domain

Quantifiers True over Domain False over Domain

True over positive real numbers, False over negative real numbers, Quantifiers True over positive real numbers, False over negative real numbers,

Validity True no matter what predicate Q is, the Domain is.

Problems Class Problems 1-3