Question -
Answer -
(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 ≤ √10
x = 0, ±1, ±2, ±3
A = {0, ±1, ±2, ±3}
(ii) B= {x : x = 1/(2n-1), 1 ≤ n ≤ 5}
Let us substitute 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, x is an integer between -1/2 and 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}.