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XI Maths, Chapter 1(Part-1).pdf

Sets, Relations and Functions

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Laishram Roshan Singh

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Page 1 :

are, fige- I, Model th. Sec. Schrol A, - Maths, CHAPTER, I-, SETS, Set: A set is a well defined cotlection of distinet objecks., The objects of the set are called elements or members f the ref., denoted, by, and while ită elements are denoted by, capital letters ég. A, B,C,X,Y, z ek, small letters eg.a;b,, A set is, nally, If a is en element of a set A, then we wrice a E A, and, a belongs to A on, a doe's not belong to A, then we write a, he words "element", "object", member" are synonymus ., say, a is in A ote a 's a member of A. If, A., The following are seme illustrakons of sets., Illutrafon /: collestrin of all teachers in a, school is a set-, Jlustraken ., The collecton of first five natural, numbers isa get., Illustraton 3: The collection of good crickel players, of India es not a set because the term " good player", es vague (unelear) and it not well defined, Illustration 4 ., The collection of good boys en a school, the collection of all boys m a, is not a ret. Honiever,, school is a set, NOTE Every, given collection, is well defened, then, otherwire, (f ret., well defened means, ote obvious, self evident, enigpe interpretaton oR value., description (Representation) of a set, A set is often described in the followeing tuo fonms, iRoster form or Tabular form, i Sef - builder fonm on Rule form, set. 4 the, et is a sef., et is not well deféned) it is not a, cotlection need not be a, clearly defined, ore described on explamed, Contel.

are, fige- I, Model th. Sec. Schrol A, - Maths, CHAPTER, I-, SETS, Set: A set is a well defined cotlection of distinet objecks., The objects of the set are called elements or members f the ref., denoted, by, and while ită elements are denoted by, capital letters ég. A, B,C,X,Y, z ek, small letters eg.a;b,, A set is, nally, If a is en element of a set A, then we wrice a E A, and, a belongs to A on, a doe's not belong to A, then we write a, he words "element", "object", member" are synonymus ., say, a is in A ote a 's a member of A. If, A., The following are seme illustrakons of sets., Illutrafon /: collestrin of all teachers in a, school is a set-, Jlustraken ., The collecton of first five natural, numbers isa get., Illustraton 3: The collection of good crickel players, of India es not a set because the term " good player", es vague (unelear) and it not well defined, Illustration 4 ., The collection of good boys en a school, the collection of all boys m a, is not a ret. Honiever,, school is a set, NOTE Every, given collection, is well defened, then, otherwire, (f ret., well defened means, ote obvious, self evident, enigpe interpretaton oR value., description (Representation) of a set, A set is often described in the followeing tuo fonms, iRoster form or Tabular form, i Sef - builder fonm on Rule form, set. 4 the, et is a sef., et is not well deféned) it is not a, cotlection need not be a, clearly defined, ore described on explamed, Contel.

Page 3 :

3., XP- MATHS., Exercise I./, 82 Let Azf 1, 2, 3, 4, 5,6? . Insert the appropriate symbol, E (belorgi to) on €, ) 5– A, ¢ daes nat belongs to) in the blank spaces., A, A, -A, (18) 2, (ui), 10, A, soln: ) 5 E A, (i) 8 E A, i), 0¢ A, (iv) 4 E A, (u) 2 € A, (vi), 10 ¢ A, 83. Wrike the followng sets in Roster formlor Tabular from)., ) A = fn: x ès an, è) B = {2:, integer and - 3s<7}, くえく7, x is a natural rumber less than 62, natural number such tHat, Rei) C =, two, t, the sum of its diğets is 8, D= {'x:z is a prime rumber uhich is divisor f.60), The set of all letters in the word TRIGONOMETRY, f2: x s a tuo digit, (v) E =, sai) A = イ-3,-2,-,0」52,3,タ)5,6, のb- {, 2,3,タ)5, ノ, ノ, 9 C= {17, 26, 35,44, 53,62,71,80, 2,3 and 5 are prime factors, of 607, Iナ7=8, 246 =8, 3 +5 = 8, i) D= {2,3,5}, ノ, 8+0=8, 6) E = {T,R, I, G,O,N, M, E, f Thy taking only ence fer repeated, letter's, 84. Wnile the follownig refs en the set builder form ., E) {3,6,9,12} "{2,4,8, lh, 32} lii){5,25,128,625), ){スウッ6) ? () { - ッ /r, soln: (☺ {3,6,9, 123= fr:x=3n, nEN and n<5}, ) {2,4,8, 14,32} = {2', 2², 2', 2", 2*}= {r: x = 2", n € N and 187., ) {5, 25, 125, 625} = {5', 5, 5; 5"} = f*:x= 5", nEN and !sns4?, ()タ6) Y= {x:X=2n )nEN, 1 (4) {l, 4,9,, o, 16725), %3D, 3

3., XP- MATHS., Exercise I./, 82 Let Azf 1, 2, 3, 4, 5,6? . Insert the appropriate symbol, E (belorgi to) on €, ) 5– A, ¢ daes nat belongs to) in the blank spaces., A, A, -A, (18) 2, (ui), 10, A, soln: ) 5 E A, (i) 8 E A, i), 0¢ A, (iv) 4 E A, (u) 2 € A, (vi), 10 ¢ A, 83. Wrike the followng sets in Roster formlor Tabular from)., ) A = fn: x ès an, è) B = {2:, integer and - 3s<7}, くえく7, x is a natural rumber less than 62, natural number such tHat, Rei) C =, two, t, the sum of its diğets is 8, D= {'x:z is a prime rumber uhich is divisor f.60), The set of all letters in the word TRIGONOMETRY, f2: x s a tuo digit, (v) E =, sai) A = イ-3,-2,-,0」52,3,タ)5,6, のb- {, 2,3,タ)5, ノ, ノ, 9 C= {17, 26, 35,44, 53,62,71,80, 2,3 and 5 are prime factors, of 607, Iナ7=8, 246 =8, 3 +5 = 8, i) D= {2,3,5}, ノ, 8+0=8, 6) E = {T,R, I, G,O,N, M, E, f Thy taking only ence fer repeated, letter's, 84. Wnile the follownig refs en the set builder form ., E) {3,6,9,12} "{2,4,8, lh, 32} lii){5,25,128,625), ){スウッ6) ? () { - ッ /r, soln: (☺ {3,6,9, 123= fr:x=3n, nEN and n<5}, ) {2,4,8, 14,32} = {2', 2², 2', 2", 2*}= {r: x = 2", n € N and 187., ) {5, 25, 125, 625} = {5', 5, 5; 5"} = f*:x= 5", nEN and !sns4?, ()タ6) Y= {x:X=2n )nEN, 1 (4) {l, 4,9,, o, 16725), %3D, 3

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