List all the elements of the following sets

(i) A={x : x²≤ 10, x ∈ Z}

First of all, x is an integer hence 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

Square root of next integers are greater than 10.

\( x ≤ \sqrt{10}\)

x = 0, ±1, ±2, ±3

A = {0, ±1, ±2, ±3}

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

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

At n=1, x = \(\dfrac{ 1}{(2(1)-1) }= \dfrac{1}{1}\)

At n=2, x = \( \dfrac{1}{3}\)

At n=3, x = \( \dfrac{1}{5}\)

At n=4, x = \( \dfrac{1}{7}\)

At n=5, x  = \( \dfrac{1}{9}\)

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

Given, x is an integer between \( \dfrac{-1}{2}\)and \( \dfrac{9}{2}\)

So all integers between -0.5

C = {0, 1, 2, 3, 4}

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

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}

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”}

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

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