"Notice that by the definition, every set is a subset of itself. Sometimes, though, it’s useful to talk about whether a set is really a subset of another, and you don’t want it to “count” if the two sets are actually equal. This is called a proper subset, and the symbol for it is ⊂. You can see the rationale for the choice of symbol, because “⊆” is kind of like “≤” for numbers, and “⊂” is like “<”. Every set is a subset (not necessarily a proper one) of Ω, because our domain of discourse by definition contains everything that can come up in conversation. Somewhat less obviously, the empty set is a subset of every set. It’s weird to think that ∅ ⊆ Q when Q has several things in it, but the definition does hold. “Every” member of ∅ (there are none) is in fact also a member of Q."