Theories, Problems, Solutions

SUVs

Crazy Horse — Thu, 11 Aug 2005 16:00:00 -0400

A recent survey of 80 auto owners indicated that 24 owned SUVs and 62 owned cars which are not SUVs. Find the number of q people who owned both an SUV and some other car.

Additional resources:

BOTW Number Theory
Stanford - Set Theory
Chaos, Fractals, and Arcadia

NOT Gates

Crazy Horse — Wed, 10 Aug 2005 11:00:00 -0400

How would a NOT gate process each of the following:

(1) 110001

(2) 10010111

(3) 1000111010

Relations

Crazy Horse — Sat, 06 Aug 2005 11:00:00 -0400

Let R be the relation on A = {4,5,6,7}defined by "x is less than y", that is, R is the relation < . Write R as a set of ordered pairs.

Set Fractal

Crazy Horse — Tue, 02 Aug 2005 16:25:57 -0400

Set fractal provided by "Chaos Theory and Fractals" by Jonathan Mendelson and Elana Blumenthal

Pretty cool stuff. They have plenty more, and fine examples of chaos theory and fractals. Definitely worth a look-see.

Set Theory

Crazy Horse — Tue, 02 Aug 2005 13:32:42 -0400

Given:

V = { M,W,F}
W = {S,SU}
X = {M,T,W,TH,F}
Y = {W,TH,F,S}

Find:

(V \ W)^c

Propositions

Crazy Horse — Tue, 26 Jul 2005 14:14:04 -0400

Verify that the proposition (p ^ q) ^ ~ (p v q) is a contradiction.

Permutations

Crazy Horse — Fri, 22 Jul 2005 23:06:24 -0400

How many ways can a judge award first, second, and third places in a contest with 20 contestants?

Combinatorial Analysis

Crazy Horse — Thu, 21 Jul 2005 11:25:34 -0400

There are twelve children in a kindergarten class. Find the number of ways that the twelve children play three different games if four children are to play each game.

For more resources related to combinatorial analysis and discrete mathematics, check out

Best Book Buys - for some books relating to combinatorial analysis

Best of the Web Math Category - lists quality sites relating to all aspects of mathematics

Combinatorics Problems - a collection of problems in combinatorics

Generating Functions - interactive introduction to generating functions

Relations

Crazy Horse — Thu, 14 Jul 2005 20:25:15 -0400

Each toss of a quarter will produce either a head or a tail. Let A = {Q, T} denote the set of outcomes. Find A³, n(A³), and explain what A³ represents.