Problem Set 3 Rules of Inference and Proof (30 pts) (a) Given premises: (1) "If is a lion, then is carnivorous." (2) "Foo is not carnivorous." Can you conclude the following? "Foo is not a lion." Let L(x) : " x is a lion." C(x) : " x is carnivorous." First, write all premises and the conclusion into symbolic form. Then use rules of inference to construct a valid argument. (10 pts) (b) Prove that if n is a positive integer, then n is odd if and only if 5n+6 is odd. (c) For the statement below, decide whether it is true or false. Prove your claim using only properties of the natural numbers. (10 pts) If nN and n2+(n+1)2=(n+2)2, then n=3. (d) Use "Proof by Contradiction" to prove that if q is a positive real number, and q is irrational, then q is irrational. (10 pts)