## Mathematical Proofs

###### We examined more complicated topics related to sets such as indexed families of sets and power sets.  Logical expressions and set identities involving indexed families of sets and power sets are analyzed and simplified.

More Sets Example 01

3/20/14

Running Time: 7:57

We analyze the logical form of a statement involving sets.  We worked similar problems previously, but the statements are slightly more complex in these problems as they involve indexed families of set, power sets, etc.

More Sets Example 02

3/20/14

Running Time: 6:43

We analyze the logical form of a statement involving sets.  We worked similar problems previously, but the statements are slightly more complex in these problems as they involve indexed families of set, power sets, etc.

More Sets Example 03

3/20/14

Running Time: 3:29

This example provides a concrete instance of a family of sets.  A family of sets is just a set, where each element of the set is itself a set.  This problem presents a specific example of a family of sets and both the union and intersection of the family of sets is computed.

More Sets Example 04

3/21/14

Running Time: 5:10

We compute the power set of the set A = {a, b, 3, d}.  The power set is denoted as P(A) and is defined as a set whose elements contain all subsets of the set A.  Thus, A is an element of P(A), {a,b} is an element of A etc.