Section 1.5
Set Operations
Propositional calculus and set theory are both instances of
an algebraic system called a
Boolean Algebra.
The operators in set theory are defined in terms of the
corresponding operator in propositional calculus
As always there m
Section 1.7
1.7.1
Set Operations
1.7 SET OPERATIONS
Geometric gures were used by John Venn (18341923) to illustrate the eect of various operations
on sets called the universal set or the domain
of discourse.
Remark: Not all set operations can be represent
Section 1.3
1.3.1
Predicates and Quantiers
1.3 PREDICATES AND QUANTIFIERS
def: Informally, a predicate is a statement
about a (possibly empty) collection of variables
over various domains. Its truth value depends
on the values of the variables in their re
Section 1.6
1.6.1
Sets
1.6 SETS
def: A set is a collection of objects. The objects
are called elements or members of the set.
notation: : x S
Example 1.6.1:
2 cfw_5, 7, , algebra, 2, 2.718
8 cfw_p : p is a prime number
SOME STANDARD SETS of NUMBERS
N = th
Section 1.4
1.4.1
Nested Quantiers
1.4 NESTED QUANTIFIERS
Example 1.4.1: Every sophomore owns a
computer or has a friend in the junior class who
owns a computer.
Domains S and J are the sophomores and the
juniors. Predicates C (u) and F (v, w) mean that
u