Test 2010, questions and answers PDF

Title	Test 2010, questions and answers
Course	Logic in Computer Science
Institution	Brock University
Pages	2
File Size	58.7 KB
File Type	PDF
Total Downloads	91
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Test 2010, questions and answers...

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COSC 5P02 - Logic in Computer Science Term Test 3

Question 1: (a) Find a derivation ¤p, ¤(p → ¤p), ¤(¤p → q) ⊢ ¤q in natural dedection. Justify the application of rules whenever necessary (box conditions) (5 marks). (b) Show that the formula (♦p ∧ ¬¤q) → ♦(p ∧ ¬q) is not valid (5 marks). Hint: A universe with three elements is sufficient. The propositional variables p and q may have the same interpretation.

Solution: (a) ¤(¤p → q) ¤E ¤p → q

¤(p → ¤p) ¤p ¤E p → ¤p p ¤E →E ¤p → E q ¤I ¤q

There is only one box in the derivation which is closed by the ¤I rule. (b) Let |M| := {a, b, c}, R = {(a, b), (a, c)}, and v(p) = v (q) = {b}. This model is visualized by GFED @ABC...