1. (20pts) Answer T or F for each of the following questions.

(a) Let S = {1, {1}, {{1}}, {{{1}}}, ...}. It follows that S 2 S = .

T F

(b) p(pq)(pqr) is an expression in conjunctive normal form.

T F

(c) In an inference rule proof, if you succeed in deriving a line with a standalone T RUE on it, then youve succeeded in proving your proposition.

T F

(d) Evaluate: n I+ : m I+ : n m 6= n! m

T F

(e) The expression k + (k + 1) = 2k + 1 is a provable loop invariant in any loop in which k is guaranteed to have a well-defined numerical value.

T F