16 subsets

The set 1, 2, 3 has 8 subsets.

Each subset contains exactly 28 elements. The intersection of any two subsets contains exactly 12 elements. The intersection of any three of the subsets contains exactly 5 elements. The intersection of all four subsets contains exactly 1 element.

In all, the set N={1,2,3,4} has 16 subsets.

There are: four subsets [1], [2], [3], [4] each containing one element, six subsets [1, 2], [1, 3], [1, 4], [2, 3], [2, 4] and [3, 4] each containing two elements, four subsets [2, 3, 4], [1, 3, 4], [1, 2, 4] and [1, 2, 3] each containing three elements.

Answer: The set {1, 2, 3} has 8 subsets. A set with ‘n’ elements in it can have 2n subsets.

If a set contains ‘n’ elements, then the number of proper subsets of the set is 2n – 1. In general, number of proper subsets of a given set = 2m – 1, where m is the number of elements.

Question 387786: How many subsets does the set {A,B,C,D,E} have? Each case has 2 possibilities, so the total number of subsets (including the empty set and {A,B,C,D,E}) is 2^5, or 32.

The empty set has just 1 subset: 1. A set with one element has 1 subset with no elements and 1 subset with one element: 1 1.

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced.

For each subset it can either contain or not contain an element. For each element, there are 2 possibilities. Multiplying these together we get 27 or 128 subsets.

1024

Listing Subsets: List all the subsets of {a, b, c}. Example: The set {a, b, c} has 8 subsets. They are: ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, and {a, b, c}.

The empty set is a subset of every set. The empty set is a proper subset of every set except for the empty set.

An empty set exists. However, any axiom of set theory or logic that implies the existence of any set will imply the existence of the empty set, if one has the axiom schema of separation. This is true, since the empty set is a subset of any set consisting of those elements that satisfy a contradictory formula.

But Ø has no elements! So Ø can’t have an element in it that is not in A, because it can’t have any elements in it at all, by definition. So it cannot be true that Ø is not a subset of A.

The set Ø = { } is the empty set containing no elements. The set ℕ = {0, 1, 2, 3, 4, … } is the set of all natural numbers. We treat 0 as a natural number. The set ℤ = {…, -2, -1, 0, 1, 2, …} is the set of all integers.

The empty (or void, or null) set, symbolized by {} or Ø, contains no elements at all. Nonetheless, it has the status of being a set.

The letter “Ø” is sometimes used in mathematics as a replacement for the symbol “∅” (Unicode character U+2205), referring to the empty set as established by Bourbaki, and sometimes in linguistics as a replacement for same symbol used to represent a zero. Slashed zero is an alternate glyph for the zero character.

If A is the empty set then A has no elements and so all of its elements (there are none) belong to B no matter what set B we are dealing with. That is, the empty set is a subset of every set.

0 neither finite or infinite. 0 cannot be measured because it has no value, and has no direction because it leads to nowhere. 0 isn’t an easy number to describe when it comes to definite or indefinite numbers. It’s sometimes considered the reciprocal of infinity.

If the set has a limited number of elements, then it is finite whereas if it has an unlimited number of elements, it is infinite. If the cardinality of the set is n(A) = n it is finite, but if the cardinality of the set n(A) = infinity then it is an infinite set.