The Boolean Algebra of Blood Donation

math

The blood types we usually talk about are determined by the presence or absence of three antigens (A, B, and Rh-D). Here’s a table, where presence of an antigen is denoted by a 1 (true) and absence, by a 0 (false).

A B Rh-D Type
0 0 0 O-
0 0 1 O+
0 1 0 B-
0 1 1 B+
1 0 0 A-
1 0 1 A+
1 1 0 AB-
1 1 1 AB+

You will reject a blood donation if it contains an antigen that your own blood does not. This is why O- is the “universal donor” (none of those antigens to reject) and AB+ is the “universal recipient” (you have them all naturally, so nothing is rejected). Let’s make a truth table for this, just for the A antigen:

Donor A Recipient A Can accept
0 0 1
0 1 1
1 0 0
1 1 1

Does that look familiar? It should; it’s the logical implication operation. So a person can receive another’s blood if the donor’s blood type bitwise implies the recipient’s blood type. Neat.

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