1. Let be an SL-formula. Prove that o is logically equivalent to -n. 2. Prove that {,v} E ^ . 3. Prove both (a) { ^ b} E and (b) { ^ v} E b. 4. Prove that E ((4 v) ). 5. Prove that the following sentential axioms are tautologies: (1) (4 $), (2) ( ( x)) (($ ) > ($ x), (3) ( ) ab) ( ). 6. (Bonus question) Recall definitions 6 and 7 in the Proof Theory section of the course notes (currently p. 27). Try to prove { v, x } F x. Hint: Use the proof of {$ , V x} E x from p. 29. 1. Let be an SL-formula. Prove that o is logically equivalent to -n. 2. Prove that {,v} E ^ . 3. Prove both (a) { ^ b} E and (b) { ^ v} E b. 4. Prove that E ((4 v) ). 5. Prove that the following sentential axioms are tautologies: (1) (4 $), (2) ( ( x)) (($ ) > ($ x), (3) ( ) ab) ( ). 6. (Bonus question) Recall definitions 6 and 7 in the Proof Theory section of the course notes (currently p. 27). Try to prove { v, x } F x. Hint: Use the proof of {$ , V x} E x from p. 29