Question

Write some sets of your choice, involving algebraic and geometrical ideas

Answer 1

2.1 INTRO DUCTI O NLook at the examples given below:1.Euclid, Pythagoras, Gauss, Leibnitz, Aryabhata, Bhaskar.2.a,e,i,o,u3.Happy, sad, angry, anxious, joyful, confused.4.Cricket, football, kho-kho, kabaddi, basketball.5.1, 3, 5, 7, 9.....What do you observe? Example 1 is a collection of names of some mathematicians,example 3 is a collection of feelings and example 2 is the collection of vowel letters in the Englishalphabet. We see that the names/ items/ objects in each example have something in common., i.e.they form a collection. Can you tell what are the collections in examples 4 and 5?We come across collections in mathematics too. For example, natural numbers, primenumbers, quadrilaterals in a plane etc. All examples seen so far are well defined collection ofobjects or ideas. A well defined collection of objects or ideas is known as a set. Set theory is acomparitively new concept in mathematics. It was developed by Georg Cantor (1845-1918).In this chapter, we will learn about sets and their properties, and what we mean when we saywell-defined, elements of a set, types of sets etc.2.2 WELL DEFI NED SETSWhat do we mean when we say that a set is a well defined collection of objects. Welldefined means that:1.All the objects in the set should have a common feature or property; and2.It should be possible to decide whether any given object belongs to the set or not.Let us understand 'well defined' through some examples. Consider the statement : Thecollection of all tall students in your class.Sets2 Downloaded from www.apteachers.in www.apteachers.in Free Distribution by A.P. GovernmentMathematic26What difficulty is caused by this statement? Here, who is tall is not clear. Richa decides thatall students taller than her are tall. Her set has five students. Yashodhara also decides that tallmeans all students taller than her. Her set has ten students. Ganpati decides that tall means everystudent whose height is more than 5 feet. His set has 3 students. We find that different people getdifferent collections. So, this collection is not well defined.Now consider the following statement : The collection of all students in your class who aretaller than 5 feet 6 inches.In this case, Richa, Yashodhara and Ganpati, all will get the same set. So, this collectionforms a well defined set.DO TH E S E1.Write 3 examples of 'sets' from your daily life.2.Some collections are given below. Tick the ones that form well defined sets.(i)Collection of all good students in your class.(ii)Red, blue, green, yellow, purple.(iii)1,2,3,4,5,6,7,....(iv)1, 8, 27, 64, 125, ....TRY THISState which of the following collections are sets.(i)All even numbers(ii)Stars in the sky(iii)The collection of odd positive integers. 1, 3, 5, .....2.3 NAMINGOF SETSAND ELEMENTSOFA SETWe usually denote a set by upper case letters, A, B, C, X, Y, Z etc. A few examples of setsin mathematics are given below.- The set of all Natural numbers is denoted by N.- The set of all Integers is denoted by Z.- The set of all Rational numbers is denoted by Q.- The set of all Real numbers is denoted by R.Notice that all the sets given above are well defined collections because given a number wecan decide whether it belongs to the set or not. Let us see some more examples of elements. Downloaded from www.apteachers.in www.apteachers.in