math set theory logic


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Venn Diagrams [Euler-Venn Diagrams]
A Venn diagram is a pictorial representation of sets by set of points in the plane. The universal set U is represented pictorially by interior of a rectangle and the other sets are represented by closed figures viz circles or ellipses or small rectangles or s..
Summary
A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the properties which are sat..
Example:
A = {3, 4, 5, 6}, B = {6, 4, 3, 5} A = B Elements in both sets need not be of same orde..
Definition:
Intersection of two sets A and B is a set whose elements belong to both A and B. ..
Rational and Irrational Numbers Introduction
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} The set of rational n..
Sequences and Series
A set of numbers arranged in a definite order according to some definite rule is called a sequence. A sequence is a function whose domain is the set N of natural numbers. Indicated sum of the terms in a sequence is called a series. The result of performing the additi..
Proof:
The null set f is a subset of every set, in particular f A. By hypothesis, A f . The two conditions imply A = f..
Venn Diagrams [Euler-Venn Diagrams]
Venn Diagrams [Euler-Venn Diagrams] - A Venn diagram is a pictorial representation of sets by set of points in the plane. The universal set U is represented pictorially by interior of a rectangle and the other sets are represented by closed figures viz circle..
Question 3
Question: Write down the following statements using set notation. (i) x is an element of set A (ii) y is not an element of set (iii) A is a subset of B (iv) A is a proper subset of B (v) A contains B (vi) A is superset of B (vii) Neither A is a subset of B, nor B ..
Associative laws
If A, B, C are three sets, then..
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