Union And Intersection Formula

To solve the practical problems related to union and intersection first we need to summarize the meaning of union intersection and difference of sets.

Union and intersection formula. This example illustrates how to use the union and intersect operator borders below for illustration only in excel. A useful way to remember the symbol is i cap tersection. We will extend the above ideas to the situation where we have three sets which we will denote a b and c. In order to perform basic probability calculations we need to review the ideas from set theory related to the set operations of union intersection and complement.

The intersection of 2 sets a a a and b b b is denoted by a b a cap b a b. We can define the union of a collection of sets as the set of all distinct elements that are in any of these sets. If a and b are sets we define their union as the set consisting of all elements that belong to a or b and denoted it by a u b is x x a or x b intersection of sets. The union of two or more sets is the set that contains all the elements of each of the sets.

The union of two sets a and b is the set of all the elements present in a or b or both. Use of formula. We will not assume anything more than this so there is the possibility that the sets have a non empty intersection. The goal will be to calculate the probability of the union of these three sets or p a u b.

Here are some useful rules and definitions for working with sets. The probability of the intersection of two events. Formula for union of 3 sets. This is the set of all distinct elements that are in both a a a and b b b.

The empty set is an identity element for the operation of union. That is a a for any set a. This version of the formula is most useful when we know the conditional probability of a given b as well as the probability of the event b. Since sets with unions and intersections form a boolean algebra intersection distributes over union.

The union operator comma adds two ranges. The sum function reduces to sum c4 d8 sum d7 e11 20. An element is in the union if it belongs to at least one of the sets. And understand the formulas related to them.

Similarly union is commutative so the sets can be written in any order. The intersection of sets a and b denoted by a b is x x a x b disjoint of sets.