# HTSEFP: Predicate logic

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 $\forall$.

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.

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.

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.

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