CSC165H1, Winter 2020
Problem Set 1
3. [7 marks] Choosing a universe and predicates. This question gets you to investigate some of the
subtleties of variable scope and precedence rules that are discussed in pp. 29-31 in the Course Notes.
(a) Consider the following two statements:
VI EN, P(x, 165) = P(x, 1)
(Statement 1)
(VI E N, P(x. 165)) = (VI E N. P(z, 1))
(Statement 2)
Provide a definition of a binary predicate Pover N x N that makes one of the above statements True
and the other statement False.' Your predicate may not be a constant function (ie., always True or
always False).
Briefly justify your response, but no formal proofs are necessary.
(b) Consider the following two statements:
VIES, BET, P(x,y) = Q(1)
(Statement 1)
VIE S. (3VET, P(x,y)) = Q(x)
(Statement 2)
Provide one definition of sets S and T, and predicates P (over 5 x 7) and Q (over $), that makes
one of the above statements True and the other statement False. Your sets must be non-empty, and
your predicates may not be constant functions (i.e., always True or always False).
Briefly justify your response, but no formal proofs are necessary.