it just one question named q2 and the answer will beq2 1a, q2 1b ,q2 1c , q2 2a, q2 2b , q2 2c , q2 3a, q23b , q2 3c, q2 4a, q24b, q2 4c
math Jeff Edmonds York University Assignment 1 MATH1090 Propositional Logic 12.12.22.32.4 a6666 b 7777 c 7777 1 Hi All, So sorry, I change things as we go. (This was way way worse the last year) What to Parse: Before today, my parse tree did not parse the oracle's subtree. I worked hard the last two day to change the slides (and the test) to parse all of the oracle's subtree except for implies ->. (This is recorded in the videos.) Today during the lecture, we all questioned why I did not parse oracle's implies ->. After class, I redid the "Humans are Mortal" example pg 210-213 to do it with parsing oracle's implies ->. (It is also still done with modus ponens as well.) (This is not recorded in the videos.) On the test: DO parse the oracle's subtree for sure. You can either use modus ponens or parsing oracle's implies ->. Your call. Tell me which you like better. Bubbling back up. See pg 209 & 214. I DO want you to do this on the test. Building a model: When trying to discover a model, start with the statement being false and work backwards to get what you need. pg 252-257 (not video recorded.) But when handing it on the test, start with your definition of the model, and then evaluate the formula as false. pg 258. You WILL have to give a few formal proofs on the test. But they should fall out with out much stress. The hard part of the proof system is not what you CAN do but knowing what you CANT do. That latter comes up when you try to prove things that are NOT valid and you must catch the mistake in the proof. You do NOT need to do this one the test. Three players: Adversary: prover: Oracle: If there is an implied "M, I go first providing worst case U, functions, relations and free vars. I prove formula is true with the Adversary’s choices and the Oracle’s help. If "x, If $y, If or, If , I assure A from AB. If "x, If $y, If or, If , provides worst x. constructs best y. chooses which side to prove. get new oracle to assure LHS. queries about his favorite x. provides best y. chooses which side to prove. assures LHS, then assures the RHS. or use modus ponens. Follow the Parse Tree 4 For each of the following, either Valid: Argue it in your own words using the pictures below. Give the parse tree and prove it valid by following the oracle, prover, adversary game. Give a formal proof. Invalid: Argue in your own words why it is not valid Give a model in which it is not true. Leave blank. Worth zero marks. Proofs with Oracle Q2 ["z [α(z)"x β(x,z)]] ["x "z [α(z)β(x,z)]] ["z [α(z)"x β(x,z)]] [α(z´)β(x´,z´)] ["z [α(z)"x β(x,z)]] [α(1)"x"z β(x,z)] ["x "z [α(z)β(x,z)]] ["z [α(z)"x β(x,z)]] 5 Proofs with Oracle Q2 β0123 0 1 2 3 T F T F F T T T T F F T T T F F x z β(x,z) α(0) α(1) α(2) α(3) ["z [α(z)"x β(x,z)]] ["x "z [α(z)β(x,z)]] ["z [α(z)"x β(x,z)]] [α(z´)β(x´,z´)] ["z [α(z)"x β(x,z)]] [α(1)"x"z β(x,z)] ["x "z [α(z)β(x,z)]] ["z [α(z)"x β(x,z)]] 6