In set theory, what does the symbol “U” represent?
(a) Intersection
(b) Difference
(c) Empty set
(d) Union
The correct answer and explanation is:
The correct answer is (d) Union.
In set theory, the symbol “U” is used to represent the union of two sets. The union of two sets is the set of elements that belong to either of the sets or to both. This means that if you take two sets, say A and B, their union is a new set that contains all the elements from A, all the elements from B, and any elements that are common to both.
Mathematically, the union of two sets A and B is denoted as A ∪ B. If you think of sets as collections of objects, the union essentially combines all the objects from both sets into one collection without any repetitions. For example, if set A is {1, 2, 3} and set B is {3, 4, 5}, the union of A and B would be {1, 2, 3, 4, 5}. Notice that the number 3, which appears in both sets, is only listed once in the union, as sets do not contain duplicate elements.
The union operation is one of the fundamental operations in set theory and is widely used in many areas of mathematics and logic. It helps in combining different sets to analyze the elements that exist in any of the sets involved.
In contrast, the other options represent different set operations:
- (a) Intersection is represented by the symbol “∩” and refers to the set of elements that are common to both sets.
- (b) Difference is represented by the symbol “−” and refers to the set of elements that are in one set but not in the other.
- (c) Empty set is denoted by “∅” and represents a set with no elements at all.
Thus, “U” specifically represents the union operation in set theory.