3x3 minesweeper with A2=2, C1=1=C3, and C2=*

A AND B SUBSET A

U={0,1,2,3,4,5,6,7,8,9,10},

A={0,1,2,3,4,5}

B={0,2,4,6,8,10}

C={2,3,5,7}

Each student is assigned one of A U B, A AND B, A' U B, A AND B AND C, A' AND B AND C, A U(B AND C), A AND (B U C), (A U B')', A \ B, B \ A, A \ (B \ C), C \ (B \ A), (A \ B) AND (C \ B), (A \ B) AND (A \ C), U' AND (A U B U C).

Minesweeper 6*6 with A1=1, A2=2, A3=2, A4=1, B4=1, C4=1. Prove that there is a mine in square B2, Intro to Computer Lab and course web pages, Web Search for Bios. presentations of proof of statement assigned in Wednesday's class.

a,b in C implies ab in C

The square of any integer is in the form 4k or 4k+1

Any integer of the form 6k+5 is of the form 3k+2, but not conversly

Disprove there exists y in R\{0} s.t. for all x in R\{0} xy=1

Prove For all x in R\{0} there exists y in R\{0} s.t. xy=1

Prove For all x,y in R, x not equal to y IMPLIES 2x+1 not equal to 2y+1 by stating and proving the contrapositive.

Hand out Problem Set 4 due Tues 22nd at 5pm

Star Trek TNG The Royale Episode 38 3/27/89, stardate 42625.4 part where Captain Pickard and Riker discuss Fermat's Last Theorem.

The Proof, NOVA, 1997 about Fermat's Last Theorem.

For all c, there exists a,b in R s.t. c in C ---> c=a+b i

There exists a,b in R s.t. for all c, c in C ---> c=a+b i

There exists a,b in R s.t. there exists c, c in C ---> c=a+b i

For all x in R, there exists y in R s.t. xy=1.

There exists y in R s.t. for all x in R, xy=1.

There exists x in R s.t. for all y in R, xy=1.

For all n in N, 2^(2n) -1 is divisible by 3.

1^2 +3^2 +5^2 +...+(2n-1)^2 = n(2n-1)(2n+1)/3 for all n in N

2^2 +4^2 +5^2 +...+(2n)^2 = 2n(n+1)(2n+1)/3 for all n in N

1/(1*2) + 1/(2*3) +1/(3*4) =... = 1/(n*n+1) = n/(n+1)

For all n in N, 2 divides 3^n-1

For all n in N, 5 divides 8^n-3^n

read p. 51-56 and do p. 56 #1,

Find the flaw in the proof that all horses are the same color. (Hint, in the induction step, trace through that part of the proof for specific small numbers k).

review demo on Sophie Germain's work on FLT,

and prove or disprove each of the following:

For all x not 0 in R, there exists y in R s.t. xy=1.

There exists y in R s.t. for all x not 0 in R, xy=1.

There exists x not 0 in R s.t. for all y in R, xy=1.

Cayley, Cauchy, Browne, and Jordan, prepare presentations.

For all x not 0 in R, there exists y in R s.t. xy=1.

There exists y in R s.t. for all x not 0 in R, xy=1.

There exists x not 0 in R s.t. for all y in R, xy=1.

Define the order of a group, abelian group. Prove that GL(2,R) is an abelian group under matrix addition, and that it is not abelian and not a group under matrix multiplication.

a,b,c in R, a not 0, ab=ac implies b=c

a,b, in R, ab=0 implies a=0 or b=0

a in R implies, a not 0, a^2 = a implies a=0 or a=1.

1) Write out the hidden quantifiers in the statement

2) Write out the negation of the statement

3) Prove the negation.

4) Prepare presentation for Wednesday

-Write down similar Maple commands to show that the other 7 commands hold: j^2=-1, k^2=-1, ji=-k , jk=i, kj=-i, ki=j, ik=-j.

-Finish this proof that H is not abelian

on WebCT Bulletin Board -Forum- Maple Demos