Homework 1
Due Wednesday, September 6 at the start of class.
- Verify the following tautologies by constructing truth tables:
- p0 v (p1 v p2) = (p0 v p1) v p2
- p0 v p1 = p1 v p0
- p0 v p0 = p0
- p0 ^ (p1 v ¬p1) = p0
- p0 ^ (p1 v p2) = (p0 ^ p1) v (p0 ^ p2)
- p0 ^ p1 = ¬(¬p0 v ¬p1)
- Using only the above logical equivalences and the laws of
algebraic reasoning, verify the following tautologies (hint: work them
in the order given so that you can use the earlier ones to help with
the later ones):
- p0 ^ p1 = p1 ^ p0
- (p0 ^ p1) v p0 = p0
- p0 v (p1 v ¬p1) = p1 v ¬p1
- ¬¬(p1 v ¬p1) = p1 v ¬p1
- p0 ^ ¬(p1 v ¬p1) = ¬(p1 v ¬p1)
- p0 v ¬(p1 v ¬p1) = p0
- ¬¬p0 = p0