Question

the table lists the eight human blood types.
it also shows how blood types determine who a person can donate blood to and receive blood from.
blood type | can donate to | can receive from
a+ | a+, ab+ | a+, a−, o+, o−
b+ | b+, ab+ | b+, b−, o+, o−
ab+ | ab+ | all blood types
ab− | ab+, ab− | a−, b−, ab−, o−
a− | a+, a−, ab+, ab− | a−, o−
b− | b+, b−, ab+, ab− | b−, o−
o+ | a+, b+, ab+, o+ | o+, o−
o− | all blood types | o−
let ( u ) be the set of all eight human blood types.
( u = {a+, b+, ab+, ab−, a−, b−, o+, o−} )
let ( x ) be the set of blood types that type ab− can receive blood from.
let ( y ) be the set of blood types that type o+ cannot receive blood from.
find the sets below. write each answer in roster form or as ( varnothing ).
(a) ( x = )
(b) ( y = )

Explanation:

Step1: Identify set X from table

From the table, AB- can receive from {A-, B-, AB-, O-}, so $X=\{A-, B-, AB-, O-\}$

Step2: Find complement of X

The universal set $U=\{A+, B+, AB+, AB-, A-, B-, O+, O-\}$. $X'$ is all elements in U not in X.
$X' = U - X = \{A+, B+, AB+, O+\}$

Step3: Identify who O+ can receive from

From the table, O+ can receive from {O+, O-}, so the set of blood types O+ cannot receive from is all elements in U not in this set.

Step4: Calculate set Y

$Y = U - \{O+, O-\} = \{A+, B+, AB+, AB-, A-, B-\}$

Answer:

(a) $\{A+, B+, AB+, O+\}$
(b) $\{A+, B+, AB+, AB-, A-, B-\}$