6. Use the rules of inference from the formula sheet to show the follow argument is valid: \x Q(x) 3x (-P(x) V Q(x))

2. Use your own predicates P(x) and Q(x) to explain why (3r, P(x)) ^ (3x, Q(x)) is not logically equivalent to 3r, (P(x) A Q(x)).

Let C(x) be the predicate " is a comedian", and let F(x) be the predicate" is funny." Match the statements below on the left to their equivalent English translations on the right. DOD Vx(F(x) ^ C(x)) Vx (F(x) → C(x)) 3x(F(x) V-C(x)) Vx-(F(x) ^ C'(x)) 3x (F(x)^-C(x)) Vx (C(x)→-F(x)) 1. All funny people are comedians. Not all funny people are comedians. 2. 3. No comedian is funny. 4. Everyone is a funny comedian. It is not the case that everyone is a funny comedian. 6. No one is a funny comedian. 5.

Prove the property a × b = -b xa of this theorem. Let a = (a₁, a2, a3) and b = (b₁, b₂, b3). Then axb= = = (−¹)| () (-1) = -b x a.