Problem 2.1. Prove that the empty set is a subset of every set.
Solution. Given any set , we need to show that only if . As the empty set contains no elements, this condition is vacuously satisfied, hence .
Problem 2.1. Prove that the empty set is a subset of every set.
Solution. Given any set , we need to show that only if . As the empty set contains no elements, this condition is vacuously satisfied, hence .
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