Maths: How Subsets Simplify Union and Intersection

Set theory gives us a precise language for describing how the number systems we use every day nest inside one another. The chain N ⊂ Z ⊂ Q ⊂ R captures a simple idea: each system is contained within the next, so every natural number is an integer, every integer is rational, and every rational number is real. Understanding these subset relationships is what lets us combine and compare sets with confidence. Two operations sit at the heart of this. The union A ∪ B gathers everything belonging to either set, while the intersection A ∩ B keeps only what the sets share. When one set is contained in another, these operations simplify elegantly: the union collapses to the larger set, and the intersection collapses to the smaller one. This mirrors the number chain directly — since Z sits inside Q, combining them changes nothing, and filtering R down to its rational elements simply returns Q.