at neither of the following statements is logically implied by the other two. (This is done by giving a structure in which the statement in question is false, while the other two are true). 1. ∀x ∀y ∀z (Pxy→

Construct proof for the following argument within the system of sentential logic: 1. ~(~D ⊃ ~C) ⊃ ~B            Premise2. ~B ⊃ A                            Premise3. (Y V C) & (~C V ~A)     Premise    /: . D V (A V Y)

Convert each of the following argu- ments into formal statements, e.g., define sentences existentially and/or universally quantified statements. Then determine which rules of logic have been applied and explain whether or not they have been ap- plied correctly. if you do the homework you will pass the final. Somebody did not pass the final. Therefore somebody did not not do the homework. If you do the homework you will pass the final. Curly did not do the homework. Therefore Curly will not pass the final. If you don’t do the homework, you won’t pass the final. Moe did the homework. Therefore Moe passed the final.

Topic: Propositional Logic Guidelines:  - type out the work (do not handwrite)  - explain everything in words and in mathematical format - provide the solution in the format asked for the question - don't have grammar mistakes - write in full sentences