Concept
What is the difference between set membership and being a subset?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"We learned that the “∈” symbol is used to indicate set membership: the element on the left is a member of the set on the right. A related but distinct notion is the idea of a subset. When we say X ⊆ Y (pronounced “X is a subset of Y”), it means that every member of X is also a member of Y. The reverse is not necessarily true, of course, otherwise “⊆” would just mean “=”. So if A = {Dad, Lizzy} and K = {Dad, Mom, Lizzy}, then we can say A ⊆ K. Be careful about the distinction between “∈” and “⊆”, which are often confused. With ∈, the thing on the left is an element, whereas with ⊆, the thing on the left is a set. This is further complicated by the fact that the element on the left-hand side of ∈ might well be a set."
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