CSC165H1F Tutorial # 2 Fall 2011
As in Tutorial 1, suppose that you are given seven di▯erent programs A;C;E;G;I;K;M, each meant to carry out
the same task, where programs C;G;K;M are written in Python and programs A;E;I are written in Java. Let
P represent the set of all programs (our \universe" or \domain"), J represent the set of all Java programs, and T
represent the set of all correct programs.
Recall that in class, we saw how set notation like \x 2 T" can be expressed in predicate notation as \T(x)", and
how this can be used to write di▯erent sentences symbolically. Make sure that you understand this correspondence
well before answering the following questions.
1. For each English sentence below, give the \standard" symbolic representation of that sentence, as discussed
in class (where all quanti▯ers are over the universe P and predicate notation is used everywhere else), then
give a second, di▯erent symbolic representation of the same sentence (where you are allowed to quantify over
di▯erent domains or to change the order of