Construct a Venn diagram representing each event. a. (not E ) b. (A or B) c. (A & B) d. (A & B

Construct a Venn diagram representing each event. a. (not E...

Key Concepts

Venn Diagram

A Venn diagram is a visual tool used in set theory and probability to illustrate the relationships between different sets. It employs overlapping circles to represent each set, enabling the depiction of intersections (common elements), unions (all elements in any set), and complements (elements not in a given set) in a clear and intuitive manner.

Complement

The complement of a set (such as not E) refers to all elements that are not included in the specified set. In a Venn diagram, the complement is represented by the area outside the circle of the set in question, indicating the exclusion of the set's elements.

Union

The union of sets, often represented by the 'or' operator (e.g., A or B), includes all elements that are in either one or both of the sets. In a Venn diagram, the union is depicted by shading all regions covered by the involved sets.

Intersection

The intersection of sets, typically indicated by the 'and' operator (e.g., A and B), consists of only those elements that are common to all the sets involved. In a Venn diagram, this corresponds to the overlapping region where the sets intersect.

Triple Intersection

When dealing with three sets (such as A, B, and C), the triple intersection represents the area where all three sets overlap. This region contains only those elements that are simultaneously members of all three sets, and it is clearly marked in a Venn diagram by the common overlapping area.

Transcript

00:03 Hi, here in this question we have to construct venn diagrams for some events, right? so the first question it is asking we have to represent, not event, not e we have to represent.

00:20 So first we have to draw a venn diagram, right? in that rectangle represent universal set we know.

00:30 Now we construct an event.

00:33 This event suppose it is representing event e.

00:36 We have to mark not e so not e means any elements outside the circle right so these are the points go note e represent so this shaded region represent not e not e we can represent by using e complement like this or e bar mechanics now that will be the answer for first part of the question in the second part it is asking us a or b.

01:10 A or b.

01:12 So basically we know a or b represent a union b.

01:19 Okay.

01:20 So how we represent this by using one diagram is.

01:22 Here you can see we have two even further a and b.

01:26 So we have to draw two circles here.

01:29 So circle a, circle b.

01:32 You can see they are overlapping here in this figure.

01:36 Overlapping means there are some common regions.

01:38 Okay.

01:39 Now, a or b means it can be element from a or it can be from b.

01:45 So we have to take both these regions.