First Assignment, September 2015 1

First Assignment, September 2015 1 PHIL 210: FIRST ASSIGNMENT, SEPTEMBER 2015 Distributed by MyCourses: Wednesday, 3oth September, 2015 Due IN CLASS: Wednesday, 7th October, 2015 Value: 12.5% Instructions There are 100 points, worth 12.5% of your final mark; the points available per question are given following the question number. Please WRITE CLEARLY, and make sure you check your answers as best you can. (It would be wise to write in pencil, so that mistakes can be erased, thus avoiding confusion both for you and for us.) When explanations are called for, keep them concise. Don’t forget to leave sufficient space for comments and corrections. DO NOT USE COVER PAGES OF YOUR OWN, NOR ANY CARDBOARD OR PLASTIC COVERS: Following the assignment itself is OUR OWN cover sheet; please fill this out and STAPLE the pages together with this cover page on top. Don’t forget to fill in your name, McGill ID, and your TA’s name as well. Please also consult the LATE POLICY outlined on the Course Description. Last, but not least, PLEASE MAKE (AND KEEP) A COPY OF YOUR ASSIGNMENT SHEET: with close to 300 students, we will have to deal with something approximating 1000 sheets of paper, and some pages inevitably get misplaced. NOTE. It should be remembered that the Assignments and Mid-Term Exam are not just assessment tests, but . NB. have a pedagogical function, in that they’re designed to push you to look into things which you might not already have looked at sufficiently closely. You may discuss the questions with your colleagues, but be sure to compose the answers yourselves, for two reasons: first, because it is the honest thing to do, and the rules of academic integrity require you to do so; second, because otherwise you cannot be sure you actually understand the answers. 1. (25) Questions about FOL languages. (10) (a) Suppose we have an FOL with names/constants a, b, c,d, 6, function symbols f (x), g(x),h(x, y), predicate symbols: P(x), Q(x),R (x, y),x = y, and the three connectives fl, A, V (and where ‘79 is used as shorthand for the negation of an identity. For each of the following, indicate whether they are simple terms or complex terms or atomic sen- tences or non-atomic sentences, and explain why, pointing out all the reasons why they fail to be so, if indeed they do. (State also whether there are the right number of brackets. If a bracket is missing, the expression is not properly formed.) 1. aV -IP(b) 7. f(g(c)) 75 d 2- P(h(a,h(g(b)76))) 8, Ana) A Q(c) 3- R(g(a),h(c,d)) N9 75 f(h(d,e)) 9- Qo9) V R((Q(C) AR(aJa» V (PU?) V 4. c R(b,a))) 5- CW) 10. P(z) = Q(c) 6- g(f(h(f(a),g(b)))) (5) (b) Do question 1.17 from p. 36 of the textbook. (5) (c) Do question 1.20 from p. 39 of the textbook. (5) ((1) Do question 1.21 from p. 39 of the textbook.