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 $\forall$.
- 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.
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.
- 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.
- 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.
- 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.
- 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