This section will introduce how to interpret and construct Venn diagrams. Then we draw a circle within the universal set and label it with the word Trees. We must count all the numbers in the Enjoying circle. To create a Venn diagram, first we draw a rectangle and label the universal set U Plants.Adding these gives 2 22 = 24 total students who are at the same place but not right handed. We see that 2 and 22 are the numbers in the same place circle but not in the right circle. To be in the same place and not be right handed, the number must be in the same place circle but not in the right circle.Thus, there are 12 15 = 27 total students who are right handed and enjoy college. Notice that the numbers 12 and 15 are in both these circles. To be right handed and enjoy college they must be in both the Right circle and the Enjoying circle.At the same place but not right handed.then the complement of a with respect to U is denoted by A ‘ or A c or U – A and is defined as the set of all those elements of U which are not in A.\)Ĭonsider the Venn Diagram below that shows the results of a study asking students whether their first college class was at the same place they are at now, whether they are right handed, and whether they are enjoying their experience at their college. Let U be the universal set and let A be a set such that A ⊂ U.The notation A ∩ B, read as A intersection B, is used to denote the intersection of two sets A and B. The intersection of A and B is the set of all those elements which belong to both A and B.The notation A U B, read as A union B, is used to denote the union of two sets A and B. The union of A and B is the set of all those elements which belong either to A or to b or to both A and B.A set is called an infinite set if it does not have a fixed number of elements.A set is called a finite set if it is either void or it has fixed number of elements.A set is said to be an empty or null or void set if it has no element.In set builder form a set is described by a characteristic property P ( x ) of its elements x. Rational Numbers – The set of rational numbers consists of numbers that can be represented in the form of $\frac. Integers – The set of integers consists of numbers such as …….-3, -2, -1, 0, 1, 2, 3……. Whole Numbers – The set of whole numbers consists of numbers starting from 0, 1, 2, 3, ……… and so on. Natural Numbers – The set of natural numbers consists of numbers starting from 1, 2, 3, ………. These numbers are standard sets of numbers based on their specific properties. In mathematics, we commonly refer to numbers as whole numbers, natural numbers etc. Hence, the collection of vowels in the English alphabet will be a, e, i, o and u. We know that the vowels are a, e, i, o and u. Venn Diagrams Example Question 1 : Data Analysis In a class, there are 15 students who like chocolate. Venn diagrams also help us to convert common English words into mathematical terms that help add precision. It generally consists of a box that represents the sample space S together with circles or ovals. 40 of them were majoring in Mathematics, 30 of them were majoring in English, 20 were majoring in Science, 7 had a double major of. A Venn diagram is a picture that represents the outcomes of an experiment. Example 2.3.5: A survey was taken of 150 University first-year students. Then for any two finite sets A and B, n(A B) n(A) n(B) n(A B). Suppose wish to create a collection of the vowels of the English alphabet. Let n(A) number of elements in the set A. If a is any other element but does not belong to the set A, it is written as a does not belong to A, which in symbolical form is written as a ∉ A. It is written as a belongs to A, which in symbolic form is written as a ∈ A. Here, by collection, we mean an aggregate of objects or things while aggregate itself means a class of things. DefinitionĪ set is a well-defined collection of objects. What are sets and how are they useful? Let us find out. Set theory and its application are regarded as one of the fundamental concepts of mathematics. The concept of set theory was initiated by German mathematician Georg Cantor (1845-1918) when he was working on “ Problems on Trigonometric Series”. The branch of mathematical logic where we learn sets and their properties is known as set theory.
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