venn diagram ?explain and it's definition
Answers
Hey mate!!!!
A Venn diagram is a diagram that shows the relationship between and among a finite collection of sets. If we have two or more sets, we can use a Venn diagram to show the logical relationship among these sets as well as the cardinality of those sets. In particular, Venn Diagrams are used to demonstrate De Morgan's Laws. Venn diagrams are also useful in illustrating relationships in statistics, probability, logic, and more.
Venn diagrams are particularly useful in helping us think carefully about set operations as they give us a visual depiction of the relationships involved.
Basic diagrams
So what does a Venn diagram look like? To draw a Venn diagram we first draw a rectangle which will contain every item we want to consider. Since it contains every item, we can refer to it as "the universe."
Suppose now we wanted a set A which is a list of numbers containing 1 up to 5, and a set B which is a list of numbers containing 6 to 10. To represent each set we use circles :
CHECK OUT THE ATTACHMENT
How about if sets A and B have something in common? We can't simply draw two separate circles, as that won't form any logical relationship between the two. As you can see below, the way to show that relationship does indeed exist, where we merge the two circles partially.
example:
In a universal set of all positive integers less than 10 let A be the set of all positive even integers less than 10 and B the set of all positive prime integers less than . Then what will the Venn diagram look like?
CHECK OUT THE ATTACHMENT
2 is the only number that belongs to both sets, so it is found in the intersection point. Also we can see 1 and 9 that and are found outside the circles but inside the rectangle or universal set .
Set Notations in Venn diagram
Venn diagrams are very useful in getting an intuition of set notations. Some common set notations and their respective diagrams are
1) read A⊂ B as A intersection B is the set of all elements that are common to both A and B
2) A ⊃ Bread as the union of A and B is set of all elements found in both sets A and B Observe that A⊂ B=A+B-A⊃B where we subtracted the intersection to account for the repetition of elements.
3) AΔB read as symmetric difference A of B and is the set of all elements in both sets excluding the intersection of the sets ( A⊂B).
4) A'read as A compliment, is the set of all elements in the universal set excluding A itself. In some books the compliment notation is represented
as A power c
The region marked in blue shows where the elements are found.
CHECK OUT THE ATTACHMENT
Hope it helps you!!
Mark as the brainliest
Answer:
there are three images I hope it will help you.Mark me as brainleast pls
