Homework 1

Due Wednesday, September 6 at the start of class.
  1. Verify the following tautologies by constructing truth tables:
    1. p0 v (p1 v p2) = (p0 v p1) v p2
    2. p0 v p1 = p1 v p0
    3. p0 v p0 = p0
    4. p0 ^ (p1 v ¬p1) = p0
    5. p0 ^ (p1 v p2) = (p0 ^ p1) v (p0 ^ p2)
    6. p0 ^ p1 = ¬(¬p0 v ¬p1)
  2. 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):
    1. p0 ^ p1 = p1 ^ p0
    2. (p0 ^ p1) v p0 = p0
    3. p0 v (p1 v ¬p1) = p1 v ¬p1
    4. ¬¬(p1 v ¬p1) = p1 v ¬p1
    5. p0 ^ ¬(p1 v ¬p1) = ¬(p1 v ¬p1)
    6. p0 v ¬(p1 v ¬p1) = p0
    7. ¬¬p0 = p0