Homework for Sept. 4, 2009
2. Show that
.
Proof: i) Show that
Let
.
. Then x 0 C or x 0 A 1 B. If x 0 C , then x 0 C c A and x 0 C c B by the
definition of union. Thus, by the definition of intersection, x 0
and so
.
ii) Show that
Let x 0
a) x 0 C and b)
Mathematical Systems
The Logical Structure of Mathematics
Undefined Terms
Axioms or Postulates
Definitions
Theorems
Example: Geometry
Undefined terms: point, line, set, between
Postulates:
1) A line is a set of points
2) There is exactly one line that con
Homework problems due Sept. 9, 2009
3. A f B if and only if Bc f Ac.
Proof 1: a) Assume that A f B and show that Bc f Ac. Let x 0 Bc. Then x B. But then x cant belong
to A, because if it did the fact that A f B would mean that x would belong to B, a contr