devotion & mathematics

Exercise 1(c) : Problems & Solutions                   1. Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:    (i) { 2, 3, 4 } ... { 1, 2, 3, 4, 5 }       Solution :         Given sets { 2, 3, 4 } and  { 1, 2, 3, 4, 5 }         Since the set { 1, 2, 3, 4, 5 } containing all the elements  2, 3, 4 , we have         { 2, 3, 4 } ⊂ { 1, 2, 3, 4, 5 }    (ii) { a, b, c } ... { b, c, d }        Solution :          Given sets are { a, b, c } & { b, c, d }.           Since ' a ' is not in the set { b, c, d }, we have              { a, b, c } ⊄ { b, c, d }    (iii) {x : x is a student of Class XI of your school} ... {x : x student of your school}        Solutiion :   ...

   Exercise 1(b) : ( problems & solutions ) :                                      1. Which of the following are examples of the null set .      (i) Set of odd natural numbers divisible by 2.        Solution :            The odd natural numbers are 1,3,5,...             Let A be the set of odd natural numbers divisible by 2.             We know no any odd number is divisible by 2.            ∴  A has no elements.             Hence A is null set.      (ii) Set of even prime numbers .         Solution :                The prime numbers are 2,3,5,7,11,13,...               Let A be the ...

 Exercise 1(a) : ( problems & solutions )   1. Which of the following are sets? Justify your answer.       (i) The collection of all the months of a year beginning with the letter J.        Solution :              Suppose A is the collection of  months of a year beginning with the letter J are January, June and               July.                ∴ A= { January, June,July }                 This A  is  well-defined i.e. it is unchanged.                        Hence A is a set.       (ii) The collection of ten most talented writers of India.        Solution :               The collection of ten most talented writers of India may vary from ...

https://youtu.be/-Z7sRAcTBRs?si=ezkfp_zlrrINstER  RESULTS ON OPEN SET:                                                                             Result :   A subset G of a metric space X is open iff it is a union of open spheres. proof :                               R   Result .    Let X be a metric space. Then i.    Any union of open sets in X is open in X and ii.   Any finite intersection of open sets in X is open in X. Result : In any metric space X, every closed sphere is a closed set. #results #open #& #closed #sets People also search for Iit mathematics  books IIT Mathematics  Questions Iit mathematics  syllabus Arihant  IIT  JEE m...