Union And Intersection Formula

This example illustrates how to use the union and intersect operator borders below for illustration only in excel.

Union and intersection formula. The union of two sets a and b is the set of all the elements present in a or b or both. 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. We will not assume anything more than this so there is the possibility that the sets have a non empty intersection.

That is a a for any set a. We will extend the above ideas to the situation where we have three sets which we will denote a b and c. A useful way to remember the symbol is i cap tersection. Since sets with unions and intersections form a boolean algebra intersection distributes over union.

This follows from analogous facts about logical disjunction. If this is the case then we can calculate the probability of the intersection of a given b by simply multiplying two other probabilities. And understand the formulas related to them. We can define the union of a collection of sets as the set of all distinct elements that are in any of these sets.

The union of two or more sets is the set that contains all the elements of each of the sets. An element is in the union if it belongs to at least one of the sets. The union operator comma adds two ranges. Similarly union is commutative so the sets can be written in any order.

Use of formula. The probability of the intersection of two events. We will take the common elements at once only. 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.

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 goal will be to calculate the probability of the union of these three sets or p a u b. The intersection of sets a and b denoted by a b is x x a x b disjoint of sets. The sum function reduces to sum c4 d8 sum d7 e11 20.

Here are some useful rules and definitions for working with sets. The empty set is an identity element for the operation of union.