UNIVERSITY OF VICTORIAAPRIL EXAMINATIONS 2016MATH 122: Logic and FoundationsCRN: 22116 (A01), 22117 (A02), 22118 (A03), and 24254 (A04)INSTRUCTORS:G. MacGillivray (A01)K. Mynhardt (A02)J. Manzer (A03 & A04)NAME:V00#:Duration: 3 Hours.Answers are to be written on the exam paper.No calculator is necessary, but a Sharp EL-510R or a Sharp EL-510RNB calculator is allowed.This exam consists of 26 questions, for a total of 80 marks. Unless otherwise specified, inorder to receive full or partial credit, you must show your work and justify your answers.There are 10 pages (numbered), not including covers.Students must count the number of pages before beginning and report any discrepancyimmediately to the invigilator.
MATH 122 A01, A02, A03, & A04 – April 201611.  Suppose the statementp↔qis false. Find all combinations of truth values forp, q,andrsuch that the statement (¬r↔p)∨(r∧ ¬q) is true.2.  Use known logical equivalences to show thatq→(p→q) is a tautology.3.  Use the blank to indicate whether each statement is True or False. No justificationis necessary.The negation of the statementp→qisp∧ ¬q.The converse of the statementp→ ¬qisp→q.The statement∃x,(x2= 2)→(2x < x) is true for the universeQ.The statement “Every picture tells a story” has a hidden existential existentialquantifier.