To understand enough about Karnaugh maps to solve this problem on 4Clojure (which hosts problems for the programming language, Clojure), I've studied the wiki articles on K-maps, Boolean Algebra, Set Theory, sets, disjoint sets, math notation, etc.
Partway through I felt I needed more skill in the fundamentals, so I looked for ways to practice my truth tables. Before examining it closely, I took the headers from the truth table explaining the Distribution Law on an OpenStax piece on Boolean algebra and filled it out. After this I compared my truth table to the author's, when I noticed he had a result that surprised me.
Compared to mine:
I get that the Distribution Law means $x(y+z)$ is supposed to equal $xy+zy$, but I'm not seeing it.
For $x = 0, y = 1,$ and $z = 1$:
- For $xy+zy$, with:
- $x\land y = 0 \land 1 = 0$
- $y \land z = 1 \land 1 = 1$
- $0 \lor 1 = 1$
- For $x(y+z)$, this should be $0$:
- $0 \land (1 \land 1) =$
- $0 \land 1 =$
- $0$
The only way to make the first $0$ is: $0 \land (1 \lor 1) \land 0 = 0$.
Is this how Boolean algebra works? Or is it the unlikely case that the author made an error?
