p.78, icon at Example 8 #1. Suppose we have the two propositions (with symbols to represent them): "It is raining (r) or I work in the yard (w)." "It is not raining (¬r) or I go to the library (1)." What conclusion can we draw from these propositions?

p.77, icon at Example 6 #1. The proposition (¬q^(p → q)) →¬p is a tautology, as the reader can check. It is the basis for the rule of inference modus tollens: ר קר Suppose we are given the propositions: “If the class finishes Chapter 2, then they have a quiz” and “The class does not have a quiz." Find a conclusion that can be drawn using modus tollens.

(a) Is it possible for an argument to be sound and have a false conclusion? Explainyour answer (in one or two sentences).(b) Is it possible for an argument to be invalid and have a true conclusion? Explainyour answer (in one or two sentences).(c) Explain what a tautology is.(d) Explain what semantic entailment is.(e) State the deduction theorem.(f) If A ⊨ B, then A, C ⊨ B. What is this feature of entailment known as?

For the following conditional statements, write (i) the contrapositive of the statement (ii) the converse of the statement, and (iii) the negation of the statement.In part (a), your answer should be written in English (not in propositional logic).For  (a), you might have to use DeMorgan’s Laws as part of the process.(a) (6 marks) If the schools are open and the roads are safe, then the game is not cancelled