For each of the premise-conclusion pairs below, give a valid step-by-step argument (proof) along with the name of the inference rule used in each step:
(a) Premise: {¬p ∨ q → r, s ∨ ¬q, ¬t, p → t, ¬p ∧ r → ¬s}, conclusion: ¬q.
(b) Premise: {¬p → r ^ ¬s, t → s, u → ¬p, ¬w, u v w}, conclusion: ¬t v w.

What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

What is the measure of the smallest angle in the diagram? 15 29 32 45