From the course: Programming Foundations: Discrete Mathematics

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Cardinality, disjointness, and partitions

Cardinality, disjointness, and partitions

From the course: Programming Foundations: Discrete Mathematics

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Cardinality, disjointness, and partitions

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- [Voiceover] Understanding Cardinality, Disjointness, and Partitions. Cardinality is the number of elements in a set. It is defined only for finite sets. What would be the cardinality of a set containing all the letter in the English alphabet? If you said 26, you're right. When working with sets, we say that two sets are disjoint if they have no elements in common. In other words, if the intersection of the sets is the empty set. Examples of disjoint sets include: students enrolled in Discreet Mathematics at 10:05 and students enrolled in Spanish at 10:05. Another example would be people living full time on the East Coast and people living full time on the West Coast. These sets do not have any elements in common. A set partition includes all disjoint subsets of a set that when combined make it whole. If we have two disjoint sets, one is the vowels and the other is the consonants, in the English alphabet, These are two partitions of the whole set which is the English alphabet. Here…

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