introduction to set theory elements

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..

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..

Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Sinc..

Union of two sets A and B is the set of all elements which are in A, or in B, or both in A and B. In Set builder form,..

Let A be any set. In order to prove that f A we must show that there is no element of f which is not present in A. And since f contains no element at all, no such element can be found out. Hence f A...

Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number system consists ..

Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Kerala..

In mathematics , a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematics . Important terms in Sets are:..

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