PMATH 330 Logic, Assignment 4
Due Fri July 5
1. (a) The following derivation shows that (P Q)R, Q (R S ) | P (Q S )R). Provide
=
justication on each line: indicate the Basic Validity Rule which was was applied, and the lines
(if any) to which it was appli
PMATH 330 Logic, Assignment 7
Not to be handed in
In this assignment, a is a constant symbol; x, y and z are variable symbols; f , g and h are
function symbols with f unary and g and h binary; and p and r are relation symbols with
p unary and r binary.
1.
PMATH 330 Logic, Solutions to Assignment 2
1. Let F = (P (QR)(P R) and G = R(P Q). Determine whether F treq G.
Solution: We make a truth-table.
P Q R R QR
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
P (QR) P R
0
1
1
1
0
1
1
1
0
1
1
1
0
PMATH 330 Logic, Solutions to Assignment 1
1. For each of the following strings, determine (with justication) whether it is a formula and, if so, then write
out a derivation indicating which rule was applied at each step.
(a) (P (QR) P )
Solution: This st
PMATH 330 Logic, Assignment 3
Due Fri June 21
1. (a) Let F = (P Q)R S . By making a truth table, convert F into CNF.
(b) Let G = (P (Q(R P ). Use truth-equivalences to convert G into CNF.
2. Let F = P Q, G = (R Q)P , H = (P R) Q and K = (QR). Determine wh
PMATH 330 Logic, Assignment 6
Due Mon July 29
1. Translate the following statements into formulas in the language of rst-order number
theory, with the addition of the unary function symbol f .
(a) x is the smallest prime factor of y , or equivalently, x i
PMATH 330 Logic, Assignment 1
Due Fri May 24
1. For each of the following strings, determine (with justication) whether it is a formula
and, if so, then write out a derivation indicating which rule was applied at each step.
(a) (P (QR) P )
(b) (P Q) (RP )