Sets, Sets, Sets

Ghostbusters counting problem - page 153 in section 3.3. Venn diagrams and the principle of inclusion/exclusion

HOMEWORK #6 HINTS/HELP/Animated GIFs ...

• Probability (Pages 156 and 161 problems).

• Sets HW questions to clarify PowerSet, sets as members of sets, sets as subsets of sets, etc.

• Animation to illustrate Venn diagrams and symmetric difference concepts. Problem 8, page 150 help. The turqoise part of the Venn diagram is the solution.

• Animation slides seen statically one frame on top of the next.

• PowerSets, elements of, subsets of: HW #5 help/hints/examples, including even and odd cardinality and some apparent symmetry of the 1, 4, 6, 4, 1 variety.

• PowerSets of cardinality 4 compared to PowerSets of cardinality 5: Strange symmetries and how 1, 4, 6, 4, 1 leads to 1, 5, 10, 10, 5, 1.

  Speaking of 1, 5, 10, 10, 5, 1:

  In any set with 5 elements, there will be 2 to the 5th power subsets or 32 elements in the PowerSet, which is the set of all possible subsets:

  • the power set elements of size 0 total 1, (the empty set),
  • the power sets of size 1 total 5,
  • the power set elements of size 2 total 10,
  • the power set elements of cardinality 3 total 10,
  • the power set elements of cardinality 4 total 5,
  • and the power set elements of cardinality 5 total 1 (the set itself).

• One more time on PowerSets concepts. The empty set is a subset of every set. Every set is a subset of itself. The empty set is a proper subset of every set, except for one set. No set is proper subset of itself!

• Representing sets as binary numbers. Representing an entire Power Set of any 3 elements as all the 3 bit binary numbers.

• Spring of 1997 Power Set mystery problems.

• Empty Sets and sets containing the empty set, and why sets containing the empty set are not empty. Rescheduled quiz email note too.

1. Pascal, Fortran, C++ freshmen engineering class of 300 students and probability thinking, Venn diagram using, principle of inclusion/exclusion wielding problem solver's feast.
2. HW #6 solution a.
3. HW #6 solution b.
4. HW #6 solution c.