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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_Through_Guided_Discovery_(Bogart)/06%3A_Groups_Acting_on_Sets/6.02%3A_Groups_Acting_on_SetsWe have seen that the fact that we have defined a permutation group as the permutations of some specific set doesn’t preclude us from thinking of the elements of that group as permuting the elements o...We have seen that the fact that we have defined a permutation group as the permutations of some specific set doesn’t preclude us from thinking of the elements of that group as permuting the elements of some other set as well.
- https://math.libretexts.org/Courses/Angelo_State_University/Finite_Mathematics/09%3A_Sets_and_Probability/9.02%3A_Union_Intersection_and_ComplementCommonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn...Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.
- https://math.libretexts.org/Courses/Rio_Hondo/Math_150%3A_Survey_of_Mathematics/03%3A_Logic/3.01%3A_Basics_of_Sets/3.1.01%3A_Union_Intersection_and_ComplementCommonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn...Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.05%3A_Combinatorics-_Inclusion_ExclusionThis page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses il...This page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses illustrates this principle. It also defines a derangement as a permutation where no element retains its original position, and concludes with practice checkpoints on related counting problems.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/04%3A_Sets/4.03%3A_Unions_and_IntersectionsWe can form a new set from existing sets by carrying out a set operation.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_1320_Finite_Mathematics_2e/08%3A_Probability/8.02%3A_Mutually_Exclusive_Events_and_the_Addition_RuleGiven two events, E, F, then finding the probability of E ∪ F, is the same as finding the probability that E will happen, or F will happen, or both will happen. Let E be the event that the numb...Given two events, E, F, then finding the probability of E ∪ F, is the same as finding the probability that E will happen, or F will happen, or both will happen. Let E be the event that the number shown on the die is an even number, and let F be the event that the number shown is greater than four. If we count the number of elements n(E) in E, and add to it the number of elements n(F) in F, the points in both E and F are counted twice, once as elements of E and once as elements of F.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/MAT_149%3A_Topics_in_Finite_Mathematics_(Holz)/04%3A_Sets_and_Counting/4.01%3A_Sets_and_Operations/4.1.02%3A_Union_Intersection_and_ComplementCommonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn...Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_310_Bridge_to_Advanced_Mathematics/01%3A_Sets/1.05%3A_Union%2C_Intersection%2C_Differenceas numbers are combined with operations such as addition, subtraction and multiplication, there are various operations that can be applied to sets. The Cartesian product is one such operation; given s...as numbers are combined with operations such as addition, subtraction and multiplication, there are various operations that can be applied to sets. The Cartesian product is one such operation; given sets A and B, we can combine them with × to get a new set A×B. Here are three new operations called union, intersection and difference.
- https://math.libretexts.org/Courses/American_River_College/Math_300%3A_My_Math_Ideas_Textbook_(Kinoshita)/04%3A_Sets/4.01%3A_Sets/4.1.02%3A_Union_Intersection_and_ComplementCommonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn...Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/07%3A_Sets_and_Venn_Diagrams/7.02%3A_Union_Intersection_and_ComplementCommonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn...Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.
- https://math.libretexts.org/Workbench/Business_Precalculus/07%3A_Sets/7.02%3A_Union_Intersection_and_ComplementCommonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn...Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.
