Quiz Solutions

Quiz Answers

1. There exists an x such that, for all y, the truth of the predicate P operating on formula f applied to x and the truth of the predicate Q operating on y implies that predicate R operating on formula f applied to y, x, and z is false. x, y, and z are variables; f is a function; P, Q, and R are predicates; the right arrow means "implies"; the line with a notch on the right means "not"; the carrot means "and"; the rest of the symbols are parentheses. Note that not all of the parentheses in the formula are strictly necessary.

2. First-order logic is different from propositional logic in that it uses quantified variables. Higher-order logic allows predicates to have predicates or functions as arguments; this essentially encompasses set theory.

3. Multiple answers for these questions, of course, exist; below are expected common answers

   • x(Cangowrong(x) → Willgowrong(x))

   • x(FoCS(x) Circuits(x))

• xy(Classtogether(x, y)) -or- xyab(((Inclass(x, a) Inclass(y, a)) (Inclass(x, b) Inclass(y, b)))

~MRG