Math 99 (Notes) encoding

To Prove:		Do:
P Þ Q		"Assume P is true," prove Q is true, or "Assume Q is false," prove P is false, or "Assume P is true and Q is false", produce a contradiction.
P Û Q		Prove (P Þ Q) Ù (Q Þ P), or prove (P Þ Q) Ù (~P Þ ~Q), or prove (~Q Þ ~P) Ù (Q Þ P), or prove (~Q Þ ~P) Ù (~P Þ ~Q)
("x)(P(x))		"Let x be an arbitrary ..." Prove P(x).
($x)(P(x))		"Take x = ..." Prove P(x) for this x.
A Í B		Prove ("xÎA)(xÎB) i.e., if xÎA then xÎB.
A = B		Prove (A Í B) Ù (B Í A).
A = Ø		Prove ("x)(xÏA) (frequently best to use proof by contradiction).
xÎAÈB		Prove (xÎA) Ú (xÎB).
xÎA Ç B		Prove (xÎA) Ù (xÎB).
xÎA - B		Prove (xÎA) Ù (xÏB).
~(P(x) Þ Q(x))	Prove ($x)(P(x) Ù ~Q(x)).
~(P(x) Û Q(x))	Prove ("x)(P(x) Ù ~Q(x)) Ú ($x)(Q(x) Ù ~P(x))
~($x)(P(x))	Prove ("x)(~P(x)).
~("x)(P(x))	Prove ($x)(~P(x)).
AËB	Prove ($x)(xÎA Ù xÏB).
A ¹ B	Prove (A Ë B) Ú (B Ë A). ie, there is an xÎA where xÏB or there is an xÎB where xÏA.
A ¹ Ø	Prove ($x)(xÎA).
xÏA È B	Prove (xÏA) Ù (xÏB).
xÏA Ç B	Prove (xÏA) Ú (xÏB).
xÏA - B	Prove (xÏA) Ú (xÎB).

Math 99 (Fall 2000) web pages Created: 28 Apr 1999 Last modified: 05 Oct 2000 12:34:44 Comments to: dpvc@union.edu

Quiz 1 Review Selected Course Notes