1. The problem statement, all variables and given/known data
I have come across the following statement which I've written for myself a long time ago, and I don't remember what is going on.:

2. Relevant equations
Boolean Squaring.

3. The attempt at a solution
Sorry for the potentially stupid question, but I've been researching how to compute ##M^{(2)}##, and the best I found was how to get an adjacency matrix from a graph, and computing ##M^2## (instead of ##M^{(2)}##).

If someone could either explain to me the ##M^{(2)}## part or point me to something that explains that, I would very much appreciate it!

"Boolean algebra" is essentially algebra on "true", "false" or, equivalently "1", "0" with the addition rules that 0+ 0= 0, 1+ 0= 0+ 1= 1, and 1+ 1= 0 and multiplication rules 0*0= 0*1= 1*0= 0 and 1*1= 1.

For 1 + 1, I think you meant 1 + 1 = 1, but that's not my problem; my problem is the parentheses around the 2 . . . what's the difference between a power within parentheses and a power that's not within parentheses (in this context)?

The matrix ##M^k## has entries which specify the number of paths of length k; that is, the element ##M^k(i,j)## is the number of length-k paths from i to j. The matrix ##M^{(k)}## just says whether there are length-k paths; that is, ##M^{(k)}(i,j)## is 0 if there are no length-k paths from i to j and is equal to 1 if there is at least one length-k path from i to j.