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Given two sets A and B, we say that A is a subset of B if every element of A is also an element of B. We write A ⊆ B to denote that A is a subset of B. For example: - {1} ⊆ {1,2,3}
- {2,2,1,3,2,1,3,2} ⊆ {1,2,3}
- { } ⊆ {1,2,3}
- Let B be the set of registered students at Boston University, and C be the set of registered students in CS-103. Then C ⊆ B.
Think about why it is true that { } ⊆ {1,2,3}. There is a somewhat subtle mathematical principle at work in this statement. That same principle is invoked by this statement: "I am friends with every 100-feet-tall person who has ever lived."
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