SetLaws

[verse] The union of A and B is the same as the union of B and A, The intersection of A and B is the same as the intersection of B and A. This expresses the commutative property of the intersection operation in set theory, indicating that the order of the sets in an intersection does not affect the result. [chorus] Union combines the sets. Intersect focuses on what they the sets have in common. The complement is all elements in the larger sample set that do not exist in the set in question. two sets are disjoint when their intersect is zero. Commutative law shows that the order of the sets do not affect the results of union or intersect operations. [verse] The union of A with B, and then with C, is equal to the union of A with the union of B and C, The intersection of A with B, and then with C, is equal to the intersection of A with the intersection of B and C. These statements describe the associative properties of the union and intersection operations in set theory, indicating that how sets are grouped in these operations does not affect the result. [chorus] Union combines the sets. Intersect focuses on what they the sets have in common. The complement is all elements in the larger sample set that do not exist in the set in question. two sets are disjoint when their intersect is zero. Commutative law shows that the order of the sets do not affect the results of union or intersect operations. Associative law shows that how sets are grouped do not affect the results of union or intersect operations. [verse] The intersection of the union of A and B with C is the same as the union of the intersection of A with C and the intersection of B with C. In other words, if you first take the union of sets A and B and then intersect that result with set C, it’s equivalent to taking the intersection of A with C and the intersection of B with C, and then taking the union of those two results. The union of the intersection of A and B with C is the same as the intersection of the union of A with C and the union of B with C. This means if you first take the intersection of A and B and then take the union of that result with C, it’s equivalent to taking the union of A with C and the union of B with C, and then finding the intersection of those two results. [chorus] Union combines the sets. Intersect focuses on what they the sets have in common. The complement is all elements in the larger sample set that do not exist in the set in question. two sets are disjoint when their intersect is zero. Commutative law shows that the order of the sets do not affect the results of union or intersect operations. Associative law shows that how sets are grouped do not affect the results of union or intersect operations. Distributive law shows that intersection distributes over union, and union distributes over intersection.