Compound Inequalities
Combine two one-dimensional constraints by keeping either their shared overlap or every value accepted by at least one of them.
What happens when x must obey two inequalities at once?
Each inequality contributes its own region. The connector tells us how to combine them: AND keeps only shared membership; OR keeps membership in either region.
This same intersection/union language will reappear later in systems, domains, probability, and set theory.
AND means survive both filters.
Take x > −2 and x ≤ 5. The first constraint accepts everything right of −2. The second accepts everything at or left of 5. The values accepted by both form one bounded interval.
The chained form compresses two comparisons around the same variable. It means exactly the intersection of the two number-line regions.
A value must satisfy both inequalities. If the regions never overlap, the solution set is empty.
A value may satisfy the first inequality, the second inequality, or both. Separated pieces can remain separated.