If we interpret $1$ as being "true" and $0$ as being "false", and $a,b \in \{0, 1\}$ (i.e., $a$ and $b$ are logical propositions) then it's easy to see that
$a \lor b = \max\{0, 1\}$ and $a \land b = \min\{0, 1\}$
Is this purely a mathematical coincidence, or is there some deep reason this is true?
In one sense it is "just coincidence": if you have a structure with only two elements, there are only so many possible binary operations to go around, so some of them necessarily have to pull double duty as analogues of things that are quite different if you consider more than two elements.
On the other hand, if you change your focus just slightly and think about greatest lower bound and least upper bound instead of min and max, then there is a fruitful correspondence between the "algebraic" and "order-theoretic" views of Boolean algebras (of which the truth algebra $\{\text{true},\text{false}\}$ is one main example).