Home MATH 318 HTSEFP: Predicate logic

HTSEFP: Predicate logic CC-BY-NC

Maintainer: admin

Note: a lot of the things overlap.

1Starting with something

You're given a $\forall$ somewhere on the left side of the $\vdash$ sign (meaning you can start your formal proof with "something" rather than nothing), and you need to prove either a specific case, an existential case, or another $\forall$.

1.1General solution

Later

1.2Examples

  • Assignment 5, question 1
  • Assignment 5, question 2

2Logical theorems with if and only if

Given a logical theorem with a $\iff$ somewhere in the middle ... prove it.

2.1General solution

Prove that the left side implies the right, then prove that the right side implies the left, then prove that if each side implies the other, the $\iff$ thing is true.

2.2Examples

  • Assignment 5, question 3

3Logical theorem or not?

Given a statement, decide whether or not it is a logical theorem. If it is, prove it; otherwise, give a counterexample.

3.1General solution

Later

3.2Examples

  • Assignment 5, question 4

4At most and at least

Given some sort of statement involving "at most" and/or "at least", translate it into a logical theorem and prove it.

4.1General solution

Later

4.2Examples

  • Assignment 6, question 2

5When equality is involved

Given some statement that has equality in it somewhere, decide whether or not it is a logical theorem. If it is, prove it; otherwise, give a counterexample.

5.1General solution

Later

5.2Examples

  • Assignment 6, question 1
  • Assignment 7, question 1
  • Assignment 7, question 2 (only requires giving a counterexample)
  • Fall 2009 final exam, question 4
  • Fall 2010 final exam, question 4