1. (20pts) Answer T or F for each of the following questions. (a) Let S = {1, {1
ID: 3732739 • Letter: 1
Question
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(p¬q)(¬p¬q¬r) 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 you’ve 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
Explanation / Answer
SOLUTIONS:-
(a) TRUE
REASON:- After calculations it will give S 2 S =
(b) TRUE
REASON:- Conjunction of 2 clauses exists here
(c) TRUE
(d) TRUE
(e) TRUE
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