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 b− can donate blood to. let y be the set of blood types that type a− cannot receive blood from. find the sets below. write each answer in roster form or as ∅. (a) x = (b) y =

Explanation:

Step1: Define universal set $U$

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

Step2: Find set $X$ (B- donors)

From table, $X = \{B+, B-, AB+, AB-\}$

Step3: Compute $X'$ (complement of $X$)

$X' = U - X = \{A+, AB+, A-, O+, O-\}$

Step4: Find A- allowed receivers

From table, A- receives: $\{A-, O-\}$

Step5: Compute $Y$ (A- non-receivers)

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

Answer:

(a) $X' = \{A+, AB+, A-, O+, O-\}$
(b) $Y = \{B+, AB+, B-, O+\}$