Question

1. (2 pts) Find the argument form for the following argument and determine whether it is valid. Can we conclude that the conclusion is true if the premises are true? If George does not have eight legs, then he is not a spider. George is a spider. .:. George has eight legs. 2. (2 pts) What rules of inference are used in this famous argument? "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." 3. (2 pts) Use rules of inference to show that the hypotheses "If it does not rain or if it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on," "If the sailing race is held, then the trophy will be awarded," and "The trophy was not awarded" imply the conclusion "It rained." 4. (2 pts) Prove, or find a counterexample: the sum of the squares of two consecutive positive integers is odd. 5. (2 pts) Prove that if n is any integer then n? + 2n +n + 4 is even Hint: do two cases: one for when n is even, and one for when n is odd.