**Maintainer:**admin

Note: a lot of the things overlap.

*1*Starting 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 $\forall$.

*1.1*General solution¶

Later

*1.2*Examples¶

- Assignment 5, question 1
- Assignment 5, question 2

*2*Logical theorems with if and only if¶

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

*2.1*General 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.

*2.2*Examples¶

- Assignment 5, question 3

*3*Logical theorem or not?¶

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

*3.1*General solution¶

Later

*3.2*Examples¶

- Assignment 5, question 4

*4*At 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.

*4.1*General solution¶

Later

*4.2*Examples¶

- Assignment 6, question 2

*5*When 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.

*5.1*General solution¶

Later

*5.2*Examples¶

- 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