List all the elements of the following sets:

(i) $$A={x : x^2≤ 10, x ∈ Z}$$

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

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

(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”}

Asked by Sakshi | 2 years ago |  89

##### Solution :-

(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}.

Answered by Sakshi | 2 years ago

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