Is Subset an Equivalence Relation? | Set Theory

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. Lesson on subsets:    • What is a Subset?   Why the empty set is a subset of every set:    • Why is the Empty Set a Subset of Every Set...   Finding the number of subsets of a set:    • Finding the Number of Subsets of a Set (Ex...   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   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... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / seanemusic