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Is Subset an Equivalence Relation? | Set Theory
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Is the subset relation on all sets and equivalence relation? If so, it must be reflexive, symmetric, and transitive! We'll prove in today's set theory lesson that subset is a reflexive relation and a transitive relation, but it is not symmetric. If A is a subset of B, we cannot conclude that B is a subset of A.
For an example of sets that violate the symmetric property, consider any proper subset A of a set B. If A is a proper subset, then A is a subset of B and B will not be a subset of A. For a more specific example, consider A = integers and B = real numbers.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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For an example of sets that violate the symmetric property, consider any proper subset A of a set B. If A is a proper subset, then A is a subset of B and B will not be a subset of A. For a more specific example, consider A = integers and B = real numbers.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
+WRATH OF MATH+
Follow Wrath of Math on...
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