Sets, Sets, Sets
Section 3.3 (Counting
and Venn Diagrams)
Ghostbusters counting problem -
page 153 in section 3.3.
Venn diagrams and the principle
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.
to illustrate Venn diagrams and symmetric difference concepts.
Problem 8, page 150 help. The turqoise part of the Venn diagram
is the solution.
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.
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
- the power set elements of size 2 total
- the power set elements of cardinality 3 total
- the power set elements of cardinality 4 total
- and the power set elements of cardinality 5 total
(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
- Spring of 1997 Power Set mystery
- Empty Sets and sets containing
the empty set, and why sets containing the empty set are not
empty. Rescheduled quiz email note too.
Finish chapter 3 (Sets)
3:25 p.m. Wednesday Oct 24th
email note. HW #6, Inductive proofs,
dominos and reasoning programs with loops and repetition structures.
Pascal, Fortran, C++ freshmen
engineering class of 300 students and probability thinking, Venn diagram
using, principle of inclusion/exclusion wielding problem solver's
- HW #6 solution a.
- HW #6 solution b.
- HW #6 solution c.