Assignment 1: Assigned September 12, due Monday, September 19 at 8:30am
  1. p.78, 1.1 (1bh) Use ~ (negation), ->, /\, and \/ to express the following declarative sentence in propositional logic; state what your respective propositional atoms p, q, etc. mean:

    (b) Robert was jealous of Yvonne, or he was not in a good mood.

    (h) Today it will rain or shine, but not both.

  2. p.78, 1.1 (2b) Make sure you fully understand the conventions of binding by reinserting as many parentheses as possible in the following proposition:
    (p -> q) /\ ~(r \/ p -> q)

  3. List all the subformulas of the formula from question 2.

  4. p.78, 1.2 (1a) Prove the sequent (p /\ q) /\ r, s /\ t |- q /\ s

  5. p.79, 1.2 (1g) Prove the sequent p |- q -> (p /\ q)

  6. p.79, 1.2 (1l) Prove the sequent p -> q, r -> s |- p \/ r -> q \/ s

  7. p.79, 1.2 (2a) Is the sequent below valid or not? If it is valid, provide a proof.
    ~p -> ~q |- q -> p