Comma Notation Meaning in Fuzzy Logic Statement

Question

I have the following statement;

$$ (A \cup B)_\alpha = A_\alpha \cup B_\alpha, (A \cap B)_\alpha = A_\alpha \cap B_\alpha $$

The minimum and maximum operators represent the intersection and union of the fuzzy sets.

$A_\alpha$ is defined as;

$$A_\alpha = \{x \in X | \mu_\alpha(x) \geq \alpha\}$$

Similar idea for $B_\alpha$.

I am not sure what the comma means between the two halves of the central statement? Appreciate any advice. Thanks

Answer 1

It is a comma as used in everyday English, used to separate clauses / statements. Nothing specific to math.

It rained today, and I bought a hat.

$(A \cup B)_\alpha$ equals $A_\alpha \cup B_\alpha$, and $(A \cap B)_\alpha$ equals $A_\alpha \cap B_\alpha$.