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Q.6 Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

       (i) {1, 2, 3, 6}                                                     (a) {x : x is a prime number and a divisor of 6}

      (ii) {2, 3}                                                             (b) {x : x is an odd natural number less than 10} 

      (iii) {M,A,T,H,E,I,C,S}                                         (c) {x : x is natural number and divisor of 6}

      (iv) {1, 3, 5, 7, 9}                                                (d) {x : x is a letter of the word MATHEMATICS}.

(i) 1,2,3,6 all are natural numbers and also divisors of 6. Hence,(i) matches with (c) (ii)  2,3 are prime numbers and are divisors of 6. Hence,(ii) matches with (a). (iii) M,A,T,H,E,I,C,S are letters of word "MATHEMATICS". Hence, (iii) matches with (d). (iv) 1,3,5,7,9 are odd natural numbers less than 10. Hence,(iv) matches with (b).

Q.5 List all the elements of the following sets :

(vi) F = {x : x is a consonant in the English alphabet which precedes k }.

The consonents in english which precedes K are : B,C,D,F,G,H,J Hence, F = {B,C,D,F,G,H,J}.

Q.5  List all the elements of the following sets:

(v) E = {x : x is a month of a year not having 31 days}

The months not having 31 days are: February April June September November It can be written as {february,April,June,September,november}

Q.5 List all the elements of the following sets:

(iv) D = {x : x is a letter in the word “LOYAL”}

LOYAL has letters L,O,Y,A. D = {x : x is a letter in the word “LOYAL”} can be written as {L,O,Y,A}.

Q.5  List all the elements of the following sets:

(iii) C = {x : x is an integer, x^{2}\leq 4}

Integers whose square is less than or equal to 4 are : -2,-1,0,1,2. Hence,it can be written as c = {-2,-1,0,1,2}.

Q5 List all the elements of the following sets:

  (ii)  B= { x : x is an integer,  \frac{-1}{2} < x< \frac{9}{2} }

Intergers between    are 0,1,2,3,4. Hence,B = {0,1,2,3,4}

Q.5 List all the elements of the following sets:

(i)  A = {x : x is an odd natural number}.

A = { x : x is an odd natural number } = {1,3,5,7,9,11,13.............}

Q.4 Write the following sets in the set builder form :

(v) {1,4,9, . . .,100}

. . . .  can be written as   

Q.4  Write the following sets in the set builder form: 

(iv)  {2, 4, 6, . . .}

This is a set of all even natural numbers. {2,4,6....} can be written as {x : x is an even natural number}

Q.4 Write the following sets in the set builder form:

 (iii) {5, 25, 125, 625}

 can be written as 

Q.4  Write the following sets in the set builder form

(ii) {2,4,8,16,32}

 can be written as  

Q.4  Write the following sets in the set builder form

(i)  {3, 6, 9, 12}

A = {3,6,9,12} This can be written as : 

Q.3  Write the following sets in roster form

(vi) F = The set of all letters in the word BETTER.

The set of letters of word BETTER are: {B,E,T,R} This can be written as: F = {B,E,T,R}

Q.3  Write the following sets in roster form

(v)  E = The set of all letters in the word TRIGONOMETRY.

Letters of word TRIGONOMETRY are:T,R,I,G,N,O,M,E,Y. This can be written as : E = {T,R,I,G,N,O,M,E,Y}

Q.3  Write the following sets in roster form

(iv) D = {x : x is a prime number which is divisor of 60}

Prime numbers which are divisor of 60 are:2,3,5. This can be written as:

Q.3 Write the following sets in roster form

(iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}

The two digit numbers having sum equal to 8 are: 17,26,35,44,53,62,71,80. This can be written as:

Q 3. Write the following sets in roster form

\left ( ii \right )B= \left \{ x:x\, is \, a\, natural\, number\, less\, than\, 6 \right \}

Natural numbers less than 6 are: 1,2,3,4,5. This can be written as:

Q 3. Write the following sets in roster form

\, \left ( i \right )\, A= \left \{ x\vdot:x\, is \, an\, integer\, and\, -3\leq x< 7 \right \}

Elements of this set are:-3,-2,-1,0,1,2,3,4,5,6. Hence ,this can be written as: A = 

Q\cdot 2\, Let A = \left \{ 1,2,3,4,5,6 \right \}.Insert\, the\, appropriate\, symbol \in or\notin in\, the\, blank\, space : 

(i) 5_____A

(ii) 8_____A

(iii) 0_____A

(iv) 4_____A

(v) 2_____A

(vi) 10____A

A =  ,the elements which lie in this set belongs to this set and others do not belong. (i) 5  A (ii) 8  A (iii) 0  A (iv) 4  A (v) 2  A (vi) 10  A

Q.1 Which of the following are sets? Justify your answer

(ix) A collection of most dangerous animals of the world.

A Collection of most dangerous animal is not well defined because the criteria of defining dangerousness of any animal can vary . Hence,it is not a set.
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