Question

question 3 of 17 (1 point) | question attempt: 3 of 3
planet | buys galaxium from | sells galaxium to
alir | alir, lamy, tixo | all eight planets
bilk | alir, bilk, piaf | alir, bilk, tixo
jas | alir, jas, piaf, sydow | jas, tixo
lamy | alir, jas, lamy, piaf | alir, lamy, tixo
piaf | alir, piaf | bilk, lamy, piaf, tixo
sydow | alir, sydow, tixo | jas, sydow, tixo
tixo | all eight planets | alir, sydow, tixo, wil
wil | alir, tixo, wil | tixo, wil
let ( u ) be the set of all eight planets.
( u = { \text{alir}, \text{bilk}, \text{jas}, \text{lamy}, \text{piaf}, \text{sydow}, \text{tixo}, \text{wil} } )
let ( x ) be the set of planets piaf sells galaxium to.
let ( y ) be the set of planets bilk does not sell galaxium to.
find the sets below. write each answer in roster form or as ( varnothing ).
(a) ( x = square )
(b) ( y = square )

Explanation:

Step1: Identify set X

From the table, Piaf sells to {Bilk, Lamy, Piaf, Tixo}, so $X=\{\text{Bilk}, \text{Lamy}, \text{Piaf}, \text{Tixo}\}$

Step2: Find complement of X

$X'$ is all planets in $U$ not in $X$.
$X' = U - X = \{\text{Alir}, \text{Jas}, \text{Sydow}, \text{Wil}\}$

Step3: Identify set Y'

From the table, Bilk sells to {Alir, Bilk, Tixo}, so $Y'$ (planets Bilk does NOT sell to) is $U - \{\text{Alir}, \text{Bilk}, \text{Tixo}\}$

Step4: Find set Y

$Y$ is the complement of $Y'$, which equals the set Bilk sells to: $Y=\{\text{Alir}, \text{Bilk}, \text{Tixo}\}$

Answer:

(a) $\{\text{Alir}, \text{Jas}, \text{Sydow}, \text{Wil}\}$
(b) $\{\text{Alir}, \text{Bilk}, \text{Tixo}\}$