CS 198:352 Internet Technology
1st Midterm Summer 2006 (Time: 120 Minutes)
Name:
SID:
Section:
For TA use only: 1 2 3 4 5 6 7 8 Total
Do not open the exam until you are told to begin. Write your nam
Natural deduction proofs
as in website (except False and
True are treated as part of the
logic rather than abbreviations
for p/\~p and ~(p/\~p) )
1
Borgida/Rosen 2016
SUMMARY: Natural Deduction Intro
Disjunctive Normal Form
Disjunctive Normal Form
Theorem: every compound proposition S can be put in
disjunctive normal form.
Solution:
Construct the truth table for the proposition S.
For each row
REVIEW
Logical Equivalences Table 6 from book
ATA
AFA
Identity
Dominati A (BC) (A B) (A C)
on
A (BC) (A B) (A C)
AAA
AAA
Idempot
ent
(A B) A B
(A B) A B
De Morgans
( A) A
Double
negation
A (A B) A
A
Set Theory summary - Fall 2016
Prof. Alex Borgida
September 6, 2016
The textbooks chapter on Sets follows the one on Logic, and so relies on
its notation and results.
This document is a brief introduc
Rules of inferences and Proofs with them!
(corrected and augmented slides!
from K. Rosen)!
Borgida/Rosen 2012!
1!
pTp
pFp
Identity
(p q) r p (q r)
(p q) r p (q r)
Associative
pTT
pFF
Dominati
on
p (q