Let p, q, r, and s be propositions. Show that the following argument is valid by using rules of inference. Show every step used and write down the justification for each. (p^q) → →r rv¬s sAp ¬q As

Use the first eight rules of inference to derive the conclusion of the symbolized argument below. FPT X 2 MP Dist 1 2 3 4 D V MT DN ( ) HS DS Trans Impl PREMISE (~F V X) (P v T) PREMISE FDP PREMISE ~P PREMISE { } [ 1 CD Equiv CONCLUSION T Simp Conj Add Exp Taut ACP DM CP Com AIP Assoc IP

If 1 is used to represent true and 0 is used to represent false, determine the symbolic proposition that is computed by the following function: def Proposition(p,q):if p == 1 and q == 1:return 1elif p == 1 and q == 0:return 0elif p == 0 and q == 1:return 0elif p == 0 and q == 0:return 1

Determine whether the logical statement is a tautology, a contradiction or neither: (p→q) → (p v q). [Hint: Use a truth table with 4 rows; you need to check the last row; all T is a tautology: all F is a contradition; a mixture of T and F is neither.] Example statement: If adopting new software leads to savings, then we'll either adopt new software or save money. The parentheses fit in the statement like this: If (adopting new software leads to savings), then (we'll either adopt new software or save money). This interpretation gives adopting new software leads to savings = If we adopt new software, then we'll save money O a. Tautology O b. Neither Oc. Contradiction