Question

List all the elements of the following sets :

(i) A = {$x:x^2\underset{–}{<}10,xϵZ$}

(ii) B = { $x:x=\frac{1}{2n-1},1\underset{–}{<}n\underset{–}{<}5$}

(iii) {$C=x:x\text{is an integer},-\frac{1}{2}<x<\frac{9}{2}$ }

(iv) D = {x : x is a vowel in the word "EQUATION"}

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

(vi) F = {x : x is a letter of the word "MISSISSIPPI" }

Answer 1

(i) The integers whose squares are less than or equal to 10 are :

$(-3{)}^2=9<10$

$(-2{)}^2=4<10$

$(-1{)}^2=1<10$

$(0{)}^2=0<10$

$(1{)}^2=1<10$

$(2{)}^2=4<10$

$(3{)}^2=9<10$

The square of other intergers are more than 10

Hence A = {$0,\pm 1,\pm 2,\pm 3$}

Or

A = {0, -1, -2, -3, 1, 2, 3}

(ii) Let's find the values of $x=\frac{1}{2n-1}$ , for $1\underset{–}{<}n\underset{–}{<}5$

$forn=1,x=\frac{1}{1}=1forn=2,x=\frac{1}{2\times 2-1}=\frac{1}{4-1}=\frac{1}{3}forn=3,x=\frac{1}{2\times 3-1}=\frac{1}{6-1}=\frac{1}{5}forn=4,x=\frac{1}{2\times 4-1}=\frac{1}{8-1}=\frac{1}{7}forn=5,x=\frac{1}{2\times -1}=\frac{1}{10-1}=\frac{1}{9}$

Hence B = {$1,\frac{1}{3},\frac{1}{5},\frac{1}{7},\frac{1}{9}$ }

(iii) The integers which lie between $\frac{-1}{2}$ and $\frac{9}{2}$ are 0, 1, 2, 3, 4

Hence C = {0, 1, 3, 4}

(iv) The vowel in the word EQUATION are E,U,A, I, O.

Since the order in which the elements of a sets are written is unmaterial , D = {A,E, I, O, U}

(v) A month has either 28, 29, 30 or 31 days. Out of the 12 months in a year, the months that have 31 days are : January, March, May, July, August, October, December.

$\therefore$ E = {February, April, June, September, November}

(vi) The distinct letters of the word 'MISSISSIPPI' are M, I, S, P

Hence F = {M,I, S, P}