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Show that each of these logical equivalences are correct using sequences of equivalences from the Page O' Logical Equivalences (not truth tables, not reasoning!). (a) q (q rightarrow (q F)) F (b) [(p rightarrow q) rightarrow r] r T For this English sentence, convert it to quantified predicates in two ways. First, use a domain of "Things" for people: second, use a domain of "People" for people. Use our "one step above Things" rule for any other items that need domains. Both versions should have the same meaning as the given sentence. At least one UA student attends each UA football game (not necessarily the same student!). Each of the following English sentences include one or more implicit quantifications. Convert them to quantified predicates that mean the same as the original sentence, using the domain(s) given. (a) The sum of two integers is an integer. Domain: Numbers. (b) Books can open new worlds. Domain: Books. For the English statement below, first convert the statement to logic, then use Generalized De Morgan's possible, and finally express the result as a Laws to move the negation as far inside the expression as conversational English sentence that also keeps the negation 'inside.' Your result should mean the same as the original, but cannot have the same wording. Not all fish are green