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

1 Answer

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

Related Questions

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

Class 11 Maths Sets View Answer

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Class 11 Maths Sets View Answer