College Math

College Math Study Guide

There are some rules to remember about the intersection of sets. 1. The intersection of a set with an empty set gives the empty set, that is A ∩ ø = ø 2. The intersection of a set with the same set is equal to the set itself, that is A ∩ A = A 3. The intersection of two sets is equal to the reverse of the intersection of two sets, that is A ∩ B = B ∩ A 4. The intersection of three sets in different combinations would also be same, that is (A ∩ B) ∩ C = A ∩ (B ∩ C) Note that whenever we use union as well as intersection together, then we have to solve the operations within parenthesis first. This is because (A ∩ B) ∪ C ≠ A ∩ (B ∪ C) Let us understand this using an example: Suppose we have the following sets: A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8} and C = {1, 3, 5, 7, 9} Then, (A ∩ B) ∪ C = {2, 4} ∪ {1, 3, 5, 7, 9} = {1, 2, 3, 4, 5, 7, 9} Now, A ∩ (B ∪ C) = {1, 2, 3, 4, 5} ∩ {1, 2, 3, 4, 5, 6, 7, 8, 9} = {1, 2, 3, 4, 5} Hence, (A ∩ B) ∪ C ≠ A ∩ (B ∪ C) We can also denote these notations using Venn diagrams, shown here:

omplement of Set: If A is a given set, then the complement of A denotes all those elements which are not in the set A. It is denoted by A’ or A C . We can show the complement of a set by the following Venn diagram:

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