Unit 13 Logic and Proofs

What is Unit 13 Logic and Proofs

q logic

• The language of propositions

  • man this is just like AA and DC operators :)

• Applications

  • Translating proprisations

• Logical Equivalences

Predicate Logic

• just like Phil 105

  • We are extending propositional logic

    • like we are using variables, because everything isn’t binary just like HS operator
      • All, every some and stuff like that

• Variables

  • expressions with variables are not propositions

    • they don’t have truth tables as they are analog

• Quantifiers

  • English words

    • all
    • some

    • the two most important quantifiers are:

      • universal quantifier: “for all” symbol $\forall$
      • existential quantifier: “there exists” $\exists$

    • Example

      • all students in this class took a class n java
        • $\exists xP(x)$

      • some students in this class took a class in java

• Worst case scenario

  • when the domain of the guy is finite we can think of the worst case scenario as the default
    • $\exists xP(x)$ loop through all x in the domain
      • if at some step, p(x) is true, then $\exists xP(x)$

• Equivalence in predicate logic

  • statements that has predicates and quantifiers are equivalently

Proofs