How to decide if two conjunctive queries cannot have any result in common Consider the following queries:

Q1: age > 18 &amp; age &lt; 24 &amp; gender = 'male'

Q2: age > 25 &amp; gender = 'male' &amp; major = 'CS'

Q3: age = 20 &amp; major = 'CS'

Clearly, given any database instance $D$, we can decide $Q1(D) \cap Q2(D) = \emptyset$ and $Q2(D) \cap Q3(D) = \emptyset$. However, we cannot decide about the result of $Q1(D) \cap Q3(D)$.

I'm aware of query containment, in where the result of one query always is a subset of the results of another query. Also, I'm aware of query equivalence, in where the results of two queries should be exactly the same given any database instance.

However, I'm looking for an algorithm/terminology for my case, where before evaluating the two queries, I can decide the intersection of their results are always empty. Indeed, due to conflicting selection conditions, they cannot have any common result.
Your example queries are not conjunctive queries in the sense I came to know them. On Wikipedia they also are defined differently. What you maybe are looking for is the boolean query evaluation problem. $Q_1(D) \cap Q_2(D)$ can be expressed as $(Q_1 \wedge Q_2)(D)$, thus deciding whether $Q_1(D) \cap Q_2(D)$ is empty is the same as deciding whether $(Q_1 \wedge Q_2)(D)$ has any solution at all.
For conjunctive queries (as defined by Wikipedia) there are algorithms, faster than the brute force method, for this problem, if the query has a certain form, for example acyclic conjunctive queries.