First Assignment, September 2015 1

First Assignment, September 2015 1
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
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.

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