CS$2233$ Discrete Mathematical Structures

Homework $7$

Due $05/01/24$ before $11$:$59$pm$.$

Justify all answers in order to receive full credit. Try to work in a pair.

$1.$ n$-$ary Relations and Their Applications $(9$ points$)$

$(1)(2$ points$)$ Which $4-$tuples are in the relation $\{($a$,$ b$,$ c$,$ d$)|$a$,$ b$,$ c$,$ and d are positive integers

with abcd $=6\}?$

$(2)(2$ points$)$ Show the resulting table when the following operation has been performed

on Table $1$ shown below. Select Department$=$Physics

$(3)(2$ points$)$ Show the resulting table when the following operation has been performed

on Table $2$ shown below. Project onto Department and Room

$(4)(3$ points$)$ Give the $1-$join of Table $3$ and Table $4$ shown below.

Table $1$

Professor Department Course #

Cruz Zoology $335$

Cruz Zoology $412$

Farber Psychology $501$

Farber Psychology $617$

Grammer Physics $544$

Grammer Physics $551$

Rosen Computer Science $518$

Rosen Mathematics $575$

Table $2$

Department Course # Room Time

Computer Science $518$ N$5212$:$00$ p$.$m$.$

Mathematics $575$ N$5023$:$00$ p$.$m$.$

Mathematics $611$ N$5214$:$00$ p$.$m$.$

Physics $544$ B$5054$:$00$ p$.$m$.$

Psychology $501$ A$1003$:$00$ p$.$m$.$

Psychology $617$ A$11011$:$00$ a$.$m$.$

Zoology $335$ A$1009$:$00$ a$.$m$.$

Zoology $412$ A$1008$:$00$ a$.$m$.$

Table $3$

Department Name ID #

Computer Science $1337$

Biology $2718$

Mathematics $3141$

Table $4$

ID # Course #

$1337$ CS $2233$

$1337$ CS $3333$

$3141$ MAT $1214$