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Exercise: 1.1
Question1. Which of the following are sets? Justify your answer.
(i) The collection of all the months of the year beginning with the letter J
Solution: The set of all the months beginning with the letter J is a set because Only three months are there i.e. January,June and July.
(ii) The collecton of ten most talented writers of India.
Solution. This is not a set because there are many talented writers in India.
(iii) A team of eleven best-cricket batsman of the world.
Solution. This is not a set because there are many best cricket player in the world and not every one like same player.
(iv) The collection of all boys in your class.
Solution. This is a set because there are few boys.
(v) The collection of all natural number less than 100.
Solution. This is a set because the numbers less than 100 are 1,2,3,4,.........,99.
(vi) The collection of all even integer.
Solution. This is a set.
(vii) The collection of novels written by Munsi Prem Chandra.
Solution. This is a set.
(viii) The collection of question in this chapter.
Solution. This is a set because there are limited questions in this chapter.
(ix) A collection of most dangerous animal of the world.
Solution. This is not a set.
Question2. Write the following sets in set builder form.
(i) A={x : x is an integer and -3 <= x<7}
Solution. A={-3,-2,-1,0,1,2,3,4,5,6}
(ii) B={x :x is a natural number less than 6}
Solution. B={1,2,3,4,5}
(iii) C={x : x is a two digit number such that the sum of its digits is 8}
Solution. C={17,26,35,44,53,62,71,80}
(iv) D={x : x is a prime number which is devisor of 60}
Solution. D={2,3,5}
(v) E=The set of all the letters of the words TRIGONOMETRY.
Solution. E={T,R,I,G,O,N,O,M,E,T,R,Y}
(VI) F=The set of all letter of the word BUTTER.
Solution. F={B,U,T,T,E,R}
Question3. Write the following in set-builder form.
(i) (3,6,9,12)
Solution. A={x :x=3n and n belongs to 1<=x<=4}
(ii) (2,4,8,16,32)
Solution. B={x : x=2n ,n belongs to N 1<=n<=5}
(iii) (5,25,125,625)
Solution. c={x : x=5n, n belongs to N, 1<=n<=4 }
(iv) (2,4,6,..........)
Solution. D={x : x is an even natural number}
(v) (1,4,9,.......100)
Solution. E={x : x=n2, n belongs to N and 1<=n<=10}