Quiz.2 (takehome)
NAME
KEY
1. What are the three parts of a function?
A function f has three parts:
(a) A domain (the set of allowable input values).
(b) A codomain (a set containing output values it may contain other
elements as well).
(c) A rule of asso

1. (20 points) Let A, B, and C be some sets in a given universe. If AnB = ADC = BC = 0,
determine (A UBUCi when [AI = 50, [BI = 500, and IC'! = 5000.
IAU BUCI = [N +lBl+ [cl "HA/)5! (AI\CJ - (8nd + (ME/1d
\J
$501-$00t50000r0 0 +0
/
2. (20 points)
a. Let

CS311 Fall 2015 Your 1
o Read each problem carefully. Clearly show all of your work and erase/ cross out any work
you do not want to be graded.
0 You are n_ot permitted to use any notes or books; and you may not use your cell phone,
iphone, ipod or ipad (

CS311 Fall 2015
o Read each problem carefully. Clearly ShOW all of your work and erase/ cross out any work
you do not want to be graded.
0 You are _no_t permitted to use any notes or books; and you may not use your cell phone,
iphone, ipod or ipad (or sim

Quiz.3 (takehome)
NAME
KEY
1. True/ False
True: f (x) A x f 1 A
True: f f 1 A A
True: A f 1 f A
True: f B A B f 1 A
2. Use the propositional interpretation and a truth table to show
(A B = A) = (B c Ac )
To streamline notation, let 1 denote true and let 0

Vose Notes: Naive Set Theory (review)
Sets are often described by indicating their elements with a comma separated list. For
example, the set
A
=
cfw_
1,
2,
3
name of set
begin list
elements
end list
contains the positive integers less than 4. Sets are w

Quiz.1 (takehome)
NAME
KEY
For all questions, let A = cfw_x | (x) and B = cfw_x | (x).
1. MATCHING: Place a letter next to each term to make a 1-1 correspondence maximizing the overall
quality of paring each term with its approximate description:
Terms:
D

Vose N ot es: I nt r oduct ion t o P r oof
(for Logicians Who Reason About Themselves, by Raymond M. Smullyan)
D efi nit ion A knight-knave island is an island in which each nat ive is classified as eit her a
knight or a knave. K night s make only t rue s

Diagrams above show structured programming control structures (we assume test c does not change
state) and their corresponding verification conditions.1
Suppose functionality f is implemented as: g followed by h. That implementation is correct
provided: