Math and Arithmetic
Geometry

# Is The intersection of two nonempty sets is always nonempty?

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Not necessarily. The odd integers and the even integers are two infinitely large sets. But their intersection is the null (empty) set.

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## Related Questions

No, because the intersection of two equivalent sets will have a union the same size as its intersection.

the intersection of two sets of elements is represented by the word: a)or b)and c)up

The intersection of two sets S and T is the set of all elements that belong to both S and T.

You normally do not have an intersection of only one set. The intersection of a set with itself is the set itself - a statement that adds little value. The intersection of two sets is the set which contains elements that are in each of the two sets.

I presume you mean intersecting. Two sets are intersecting if they have members in common. The set of members common to two (or more) sets is called the intersection of those sets. If two sets have no members in common, their intersection is the empty set. In this case the sets are called disjoint.

The set of elements that are elements of the two (or more) given sets is called the intersection of the sets.

No. It can be infinite, finite or null. The set of odd integers is infinite, the set of even integers is infinite. Their intersection is void, or the null set.

It shows the intersection of two sets; those elements that are common to both sets.

Given two or more sets there is a set which is their union and a set which is there intersection. But, there is no such thing as a "union intersection set", as required for the answer to the question.

For two sets, the Venn diagram will consist of two overlapping ovals. The area of the overlap is the intersection. The entire area of both ovals is the union.

The intersection of two sets, X and Y, consists of all elements that belong to both X and Y.

You need two sets to have an intersection. If you have two sets, call them R and S, then their intersection is the set T that contains all elements of R that also belong to S OR all elements of S and also belong to R...it's the same thing.

ONLY a line can be formed by the intersection of two planes...and always.

YES. The intersection of two planes always makes a line. A line is at least two points.

Suppose A is a subset of S. Then the complement of subset A in S consists of all elements of S that are not in A. The intersection of two sets A and B consists of all elements that are in A as well as in B.

The concept of closure: If A and B are sets the intersection of sets is a set. Then if the intersection of two sets is a set and that set could be empty but still a set. The same for union, a set A union set Null is a set by closure,and is the set A.

The intersection of two lines is always a point or the line itself. The intersection of a line with plane also the same as above.

An intersection is the region of space that forms when two forms overlap (the intersection of two lines makes a point, the intersection of two planes makes a line, etc.). In set theory, it is the set formed when two or more sets overlap in terms of common elements. With respect to roads, it is the place where two roads cross each other.

Because they are disjoint, (ie. they contain none of the same elements) their intersection (what they both share in common) is the empty or null set.

It is used in set theory to indicate intersection. The intersection of two sets, A and B, is the set of all elements that are in A as well as in B.

For two sets, the Venn diagram will consist of two overlapping ovals. The area of the overlap is the intersection. The entire area of both ovals is the union.

ExplanationFormally, two sets A and B are disjoint if their intersection is the empty set, i.e. if This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i &isin; I} is pairwise disjoint if for any i and j in I with i &ne; j,For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.A partition of a set X is any collection of non-empty subsets {Ai : i &isin; I} of X such that {Ai} are pairwise disjoint andSets that are not the same.

It represents the intersection of two sets. In the context of two (or more) statements both (all) must be true.

The intersection of two planes is one straight line.

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