Question

List all the elements of the following sets:

(i) A={x : x² ≤ 10, x ∈ Z}

(ii) B = {x : x = 1/(2n-1), 1 ≤ n ≤ 5}

(iii) C = {x : x is an integer, -1/2 < x < 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) A = {x : x² ≤ 10, x ∈ Z}

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

x² ≤ 10

(-3)² = 9 < 10

(-2)² = 4 < 10

(-1)² = 1 < 10

0² = 0 < 10

1² = 1 < 10

2² = 4 < 10

3² = 9 < 10

The square root of next integers are greater than 10.

x ≤ √10

x = 0, ±1, ±2, ±3

A = {0, ±1, ±2, ±3}

(ii) B = {x : x = 1/(2n-1), 1 ≤ n ≤ 5}

Let us substituting 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 

∴ B = {1, 1/3, 1/5, 1/7, 1/9}

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

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

Therefore,  all integers between -0.5<x<4.5 are = 0, 1, 2, 3, 4

∴ C = {0, 1, 2, 3, 4}

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

Here, all vowels in the word ‘EQUATION’ are E, U, A, I, O

∴ D = {A, E, I, O, U}

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

Since, 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.

∴ E: {February, April, June, September, November}

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

Since, letters in word ‘MISSISSIPPI’ are M, I, S, P.

∴ F = {M, I, S, P}.