1. Use a truth table to determine if the following argument is valid. p Aq > r '. ~ r >~ pv ~ q 2. A set of premises and a conclusion are given. Use rules of inference to deduce the conclusion from the premises, giving a reason for each step. (a) qu (b) p>~q (c) s>t (d) f)$AU (e) P (f) r 3. Let D be the set of students at Chabot, let A(s) be "5 is an art major': and let 3(5) be "5 is taking a biology course". Express each of the following statements using quantiers, variables, and the predicates MS) and 3(5). (a) No art majors are taking a biology course. (h) Only art majors are taking a biology course. (c) Some art majors are not taking a biology course. 4. For the following statement write the contrapositive, converse, and inverse. In each case indicate if the statement is true or false. V real numberx, ifx =rr/2 then sinx =1