Power sets

The subset in constructing the power set

Remember that the empty set is a subset of each set

Power set is a set of all the subsets of a set

Therefore the empty set is always a member of the power set

Also distinguish between , which is the empty set and which is a set containing the empty set

The cardinality of the power set is where n = the cardinality of the set

Cartesian products

A X B, where A and B are sets is a set of

Ordered pairs where each pair has an element from each set in a particular order

Mathematically denoted as A X B =

Elements that can be in the 1^st position in the ordered pair must be a member of A, and likewise elements that can be in the second position must come from set B

Elements have distinct roles and therefore must be placed in the right position in the n-tuple.

Set Operations

Distinguish between set operations and set comparisons

Set operations produce sets, comparisons do not

List- look up definitions out of the book.

Union,

Intersection

Difference

Complement

Proving set identies

4 ways to prove

Argument – Example 10, pg 49

Prove A is a subset of B and B is a subset of A

Set Builder notation and Logical equivalences Represent Set with set builder notation and propositions, pg 50

Do series of substituting logical equivalences

Translate back to sets

Membership tables, pg 50

Substitute with other set identities, pg 51

Computer representation

Use integers

Each bit position in the integer is an element

0 means it is not an element/1 means it is an element