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Question -

List all the elements of the following sets:
(i) A={x : x2тЙд 10, x тИИ Z}
(ii) B = {x : x = 1/(2n-1), 1 тЙд n тЙд 5}
(iii) C = {x : x is an integer, -1/2 < x < 9/2}
(iv) D={x : x is a vowel in the word тАЬEQUATIONтАЭ}
(v) E = {x : x is a month of a year not having 31 days}
(vi) F={x : x is a letter of the word тАЬMISSISSIPPIтАЭ}



Answer -

(i)┬аA={x: x2тЙд┬а10, x тИИZ}

First of all, x is an integer hence it can be positive and negative also.

x2┬атЙд 10

(-3)2┬а= 9 < 10

(-2)2┬а= 4 < 10

(-1)2┬а= 1 < 10

02┬а= 0 < 10

12┬а= 1 < 10

22┬а= 4 < 10

32┬а= 9 < 10

Square root of next integers are greater than 10.

x тЙд тИЪ10

x = 0, ┬▒1, ┬▒2, ┬▒3

A = {0, ┬▒1, ┬▒2, ┬▒3}

(ii)┬аB= {x : x = 1/(2n-1), 1 тЙд n тЙд 5}

Let us substitute the value of n to find the values of x.

At n=1, x = 1/(2(1)-1) = 1/1

At n=2, x = 1/(2(2)-1) = 1/3

At n=3, x = 1/(2(3)-1) = 1/5

At n=4, x = 1/(2(4)-1) = 1/7

At n=5, x = 1/(2(5)-1) = 1/9

x = 1, 1/3, 1/5, 1/7, 1/9

тИ┤B = {1, 1/3, 1/5, 1/7, 1/9}

(iii)┬аC= {x : x is an integer, -1/2 < x < 9/2}

Given, x is an integer between -1/2 and 9/2

So all integers between -0.5

тИ┤┬аC= {0, 1, 2, 3, 4}

(iv)┬аD={x: x is a vowel in the word тАЬEQUATIONтАЭ}

All vowels in the word тАШEQUATIONтАЩ are E, U, A, I, O

тИ┤┬аD= {A, E, I, O, U}

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

A month has either 28, 29, 30, 31 days.

Out of 12 months in a year which are not having 31 days are:

February, April, June, September, November.

тИ┤E: {February, April, June, September, November}

(vi)┬аF= {x : x is a letter of the word тАЬMISSISSIPPIтАЭ}

Letters in word тАШMISSISSIPPIтАЩ are M, I, S, P.

тИ┤F = {M, I, S, P}.

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