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Q: How does cardinality relates to number of subset of a set?

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Cardinality is simply the number of elements of a given set. You can use the cardinality of a set to determine which elements will go into the subset. Every element in the subset must come from the cardinality of the original set. For example, a set may contain {a,b,c,d} which makes the cardinality 4. You can choose any of those elements to form a subset. Examples of subsets may be {a,c} {a, b, c} etc.

Assuming no restrictions on the set, the cardinality of a set, n, is related in this form # of subsets = 2n

The cardinality of a set is the number of elements in the set.

00 is not a set but the number zero written as a 2-digit number. The set {00} has cardinality 1.

The cardinality of a finite set is the number of elements in the set. The cardinality of infinite sets is infinity but - if you really want to go into it - reflects a measure of the degree of...

The cardinality of a finite set is the number of elements in the set. The cardinality of infinite sets is infinity but - if you really want to go into it - reflects a measure of the degree of...

The cardinality of 15 is equal to the number of elements in the set. Since 15 is only one number, its cardinality is 1.

The cardinality of a set is the number of elements in the set.

Two sets are equivalent if they have the same cardinality. For finite sets this means that they must have the same number of distinct elements. For infinite sets, equal cardinality means that there must be a one-to-one mapping from one set to the other. This can lead to some counter-intuitive results. For example, the cardinality of the set of integers is the same as the cardinality of the set of even integers although the second set is a proper subset of the first. The relevant mapping is x -> 2x.

even though its carnality is 0 one of its properties says that the only subset of the null set is the empty set * * * * * Carnality refers to sexual desires and I would be greatly surprised if the null set had any of those! The number of subsets of a set whose cardinality is C(S) is 2C(S). The cardinality of the null set is, as the answer was trying to say, 0. So the number of its subsets is 2C(S) = 20 = 1. A null set has one subset - which is also a null set.

It is a proper subset of every set other than itself. Its cardinality (size) is 0. It is unique (the only set with no elements).

Although infinite in number, they are very much a minor subset of the real numbers. If A denotes the number cardinality of rational numbers (the size of the set), then the cardinality of irrational numbers is 2A. In mathematics, A is "Aleph-null" but I cannot get this xenophobic browser to accept characters from other languages.

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