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Q: Do sets always have an intersection that is not the empty set?

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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.

Union 'U' is both sets made into one larger set. Intersection 'N' is the terms common to both sets. e.g. Set A { 1, 2, 4.} Set B { 1, 3, 5} The Union is A 'U' B = { 1,1,2,3,4,5} The Intersection is A 'N' B = { 1,1}

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 ∈ I} is pairwise disjoint if for any i and j in I with i ≠ 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 ∈ I} of X such that {Ai} are pairwise disjoint andSets that are not the same.

union means to group the given sets. where as intersection means to pick out the common elements from the given sets. if set a has 1,2,3 elements and B has 1,2,3,4,5. then its union will have 1,2,3,4,5 as its elements. and its intersection will have 1,2,3 as its elements.

The collection of all sets minus the empty set is not a set (it is too big to be a set) but instead a proper class. See Russell's paradox for why it would be problematic to consider this a set. According to axioms of standard ZFC set theory, not every intuitive "collection" of sets is a set; we must proceed carefully when reasoning about what is a set according to ZFC.

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No, only if both sets are empty. The intersection of disjoint sets is always empty.

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.

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

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.

Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.

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.

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.

empty set or null set is a set with no element.

Union 'U' is both sets made into one larger set. Intersection 'N' is the terms common to both sets. e.g. Set A { 1, 2, 4.} Set B { 1, 3, 5} The Union is A 'U' B = { 1,1,2,3,4,5} The Intersection is A 'N' B = { 1,1}

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.

Disjoint sets are sets whose intersection, denoted by an inverted U), produces the null or the empty set. If a set is not disjoint, then it is called joint. [ex. M= {1,2,A} N = {4,5,B}. S intersection D is a null set, so M and N are disjoint sets.

is the result after doing intersection on 2 or more sets. It contains the elements which are common to all the sets on which intersection were done.

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