Question

the table lists eight planets that produce galaxium. it also shows the buying and selling arrangements for galaxium among the planets.
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 bilk buys galaxium from.
let ( y ) be the set of planets tixo does not sell galaxium to.
find the sets below. write each answer in roster form or as ( varnothing ).
(a) ( x = { \text{jas}, \text{lamy}, \text{sydow}, \text{tixo}, \text{wil} }
try one last time jas, lamy, piaf }

Explanation:

Step1: Identify set X

From the table, Bilk buys galaxium from Alir, Bilk, Piaf. So $X = \{\text{Alir}, \text{Bilk}, \text{Piaf}\}$

Step2: Find complement of X

The universal set $U = \{\text{Alir}, \text{Bilk}, \text{Jas}, \text{Lamy}, \text{Piaf}, \text{Sydow}, \text{Tixo}, \text{Wil}\}$. $X'$ is all elements in $U$ not in $X$.
$X' = U - X = \{\text{Jas}, \text{Lamy}, \text{Sydow}, \text{Tixo}, \text{Wil}\}$

Step3: Identify set Y (Tixo's sales)

From the table, Tixo sells to Alir, Sydow, Tixo, Wil. So $Y = \{\text{Alir}, \text{Sydow}, \text{Tixo}, \text{Wil}\}$

Step4: Find complement of Y

$Y'$ is all elements in $U$ not in $Y$.
$Y' = U - Y = \{\text{Bilk}, \text{Jas}, \text{Lamy}, \text{Piaf}\}$

Answer:

(a) $X' = \{\text{Jas}, \text{Lamy}, \text{Sydow}, \text{Tixo}, \text{Wil}\}$
(b) $Y' = \{\text{Bilk}, \text{Jas}, \text{Lamy}, \text{Piaf}\}$