The empty set is the (unique) set [math]\emptyset[/math] for which the statement [math]x\in\emptyset[/math] is always false. General Property: A ∪ ∅ = ∅ ∪ A = A. We next illustrate with examples. Union With the Empty Set . Some examples of null sets are: The set of dogs with six legs. Here is what I need help with; A U {} = A, where U represents union and {} represents empty set Here is what I have so far: To prove this, I need to show that A U {} is a subset of A and that A is a subset of A U {}. We write A ∪ B Basically, we find A ∪ B by putting all the elements of A and B together. The union of two sets A and B is the set of elements, which are in A or in B or in both. Example #1. We call a set with no elements the null or empty set. If I can do that, then they are equal, by definition. It is represented by the symbol { } or Ø. Example: Let A = {3, 7, 11} and B = {x: x is a natural number less than 0}. Union Of Sets. +++ IMPORTANT >> And . Identity Property for Union: The Identity Property for Union says that the union of a set and the empty set is the set, i.e., union of a set with the empty set includes all the members of the set. (2) Set "Q" cannot be equal to Set "V". The set of squares with 5 sides. Definition: Given two sets A and B, the union is the set that contains elements or objects that belong to either A or to B or to both. The following table gives some properties of Union of Sets: Commutative, Associative, Identity and Distributive. There are some sets that do not contain any element at all. The empty set is the set with no elements. For example, the set of months with 32 days. It is denoted by A ∪ B and is read ‘A union B’. One basic identity that involves the union shows us what happens when we take the union of any set with the empty set, denoted by #8709. So joining this to any other set will have no effect. In, Set Theory We consider two sets as equal or similar when they have equal number of objects in it or we say , if their cardinality is same. Example: Scroll down the page for more examples. I am doing some non-homework exercises. . (Set "Q" must have a smaller number of elements than Set "V") The math symbol ⊂ is equivalent to and is interchangeable with ⊊ (the equal sign at the bottom edge of the symbol is crossed out, indicating the subset cannot be equal to the set). . The Null Set Or Empty Set.