Construct a proof with Predicate Logic

Construct a formal proof of the attached argument using the 9 rules of inference, the ten rules of replacement and quantitative/predicate logic.

Predicate Logic Proofs

I am looking for help with Predicate and Quantitative Logic. Provide proofs for the attached 4 problems using the 9 rules of inference, the 10 rules of replacement and Quantitative logic. --- Provide proof s for the following four arguments using: The 9 rules of inference; Modus Pollens (MP); Modus Tollens (MT); Hypothetical Syllogism (HS); Disjunctive Syllogism (DS); Constructive Dilemna (CD); Absorption (Abs); Simplification (Simp); Conjuction (Conj); and Addition (Add) The 10 rules of replacement: DeMorgans Theorems (DeM); Commutation (Com); Association (Assoc); Distribution (Dist);Double Negation (DN); Transposition (Trans); Implication (Impl); Equivalence (Equiv); Expor... click for more

Valid or invalid

Madeline must have known the material for the test, because if a person knows the material, that person will always get an A, and Madeline was one of the students that got an A.

Symbolic Logic

Prove the following argument: It is false that both Arthur is not anxious and Billy is not boisterous If Xavier is difficult and Billy is boisterous then Penelope is a prude If Xavier is not difficult then Arthur is anxious Arthur is not anxious Therefore, it is false that if Xavier is difficult then Penelope is not a prude.

What is the Dutch book argument for the firs axiom of probability?

What is Dutch book argument for the first axiom of probability (the one that says that the probability of a sentence is never less than 0 or more than 1)? Anyone know that theory?