1) Determine if the following deduction rule is valid:
p→q q→r ———- ∴p→r
2) Determine if the following deduction rule is valid:
p → (q ∨ r) ∼ (p → q) ————- ∴r
3) Prove or disprove the following statement. For all integers, if a is odd, then a4 is odd.
4)Prove or disprove the following statement. The difference of two perfect squares is not a prime number. Here is the reasoning for the claim: a2 − b2 = (a + b)(a − b), which is a composite number.
5) Prove by contradiction that there are no integers x and y such that x2 = 4y + 2. (Hint: For this problem, you can assume without giving proof that if x2 is even, then x is even. )
