Mathematics

y 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.