Assignment 1:Assigned September 12, due Monday, September 19 at 8:30am

- 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.

- 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)

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

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

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

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

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

~p -> ~q |- q -> p