(i) {A,P,L,E} (i) {x : x+5=5, x ∈ z} (ii) {5,-5} (ii) {x : x is a prime natural number and a divisor of 10} (iii) {0} (iii) {x : x is a letter of the word “RAJASTHAN”} (iv) {1, 2, 5, 10} (iv) {x : x...
Write the set of all vowels in the English alphabet which precede q.
The set of all vowels which precede the letter q = A, E, I, O Then, the set of this can be written as, ∴ X = {A, E, I, O}.
Write the set of all positive integers whose cube is odd.
Given, All odd number has an odd cube. Odd numbers = 2n+1. {2n+1: n ∈ Z, n>0} ∴ The set of all positive integers whose cube is odd = {1,3,5,7,……}
Write the set {1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50} in the set-builder form.
Set Builder form = {n/(n2+1): n ∈ N, 1≤ n≤ 7} In this, 12 + 1 => 2 22 + 1 => 5 32 + 1 => 10 . . 72 + 1 => 50 The denominator is the square of the numerator +1. The set builder form can...
List all the elements of the following sets: (i) E = {x : x is a month of a year not having 31 days} (ii) F={x : x is a letter of the word “MISSISSIPPI”}
Answers: (i) E = {x : x is a month of a year not having 31 days} The months may have 28, 29, 30, 31 days. Months having 31 days are February, April, June, September, November. ∴ E: {February, April,...
List all the elements of the following sets: (i) C = {x : x is an integer, -1/2 < x < 9/2} (ii) D={x : x is a vowel in the word “EQUATION”}
Answers: (i) x - integer and is between -1/2 and 9/2 Then, x = 0, 1, 2, 3, 4 ∴ C = {0, 1, 2, 3, 4} (ii) The vowels in the word ‘EQUATION’ = E, U, A, I, O ∴ D = {A, E, I, O,...
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}
Answers: (i) x - integer (+ or -) 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...
Describe the following sets in set-builder form: (i) A = {1, 2, 3, 4, 5, 6} (ii) B = {1, 1/2, 1/3, 1/4, 1/5, …..}
Answers: (i) Set-builder form of A = {x : x ∈ N, x<7} This set builder form can be explained as x is such that x belongs to the natural number also is less than 7. (ii) Set-builder form of B =...
Describe the following sets in set-builder form: (i) C = {0, 3, 6, 9, 12,….} (ii) D = {10, 11, 12, 13, 14, 15}
Answers: (i) Set-builder form of C = {x : x = 3n, n ∈ Z+} Z+ - the set of positive integers This set builder form can be explained as x is such that C is the set of multiples of 3 including 0. (ii)...
Describe the following sets in set-builder form: (i) E = {0} (ii) {1, 4, 9, 16,…,100}
Answers: (i) Set-builder form of E = {x : x = 0} This set builder form can be explained as x is such that E is an integer which is equal to 0. (ii) Set-builder form = {x2: x ∈ N, 1≤ x ≤10} In this,...
Describe the following sets in set-builder form: (i) {2, 4, 6, 8,….} (ii) {5, 25, 125, 625}
Answers: (i) Set-builder form = {x: x = 2n, n ∈ N} This set builder form can be explained as x is such that the given set are multiples of 2. (ii) Set-builder form = {5n: n ∈ N, 1≤ n ≤ 4} In this,...
Describe the following sets in Roster form: (i) The set of all letters in the word ‘Better.’
Answers: (i) The repetition of letter is not allowed in a set Then, Better = b, e, t, r ∴ Roster form = {b, e, t, r}
Describe the following sets in Roster form: (i) {x : x is a two digit number such that the sum of its digits is 8} (ii) The set of all letters in the word ‘Trigonometry’
Answers: (i) x is a 2 digit number. The sum of the digits in x is 8 Then, x = 17, 26, 35, 44, 53, 62, 71, 80 ∴ Roster form = {17, 26, 35, 44, 53, 62, 71, 80}. (ii) The repetition of a letter is...
Describe the following sets in Roster form: (i) {x ∈ R: x > x} (ii) {x : x is a prime number which is a divisor of 60}
Answers: (i) Real number = it's value Then, the roster form of real numbers which has less value than itself has no such numbers. ∴ Roster form = ϕ. Type of set - Null. (ii) x is a prime number...
Describe the following sets in Roster form: (i) {x ∈ N: x is a prime number, 10 < x < 20} (ii) {x ∈ N: x = 2n, n ∈ N}
Answers: (i) x ∈ N (x - natural number) x is a prime number between 10 and 20 Then, the prime numbers between 10 and 20 are 11,13,17,19. ∴ Roster form = {11,13,17,19}. (ii) x ∈ N (x - natural...
Which of the following are examples of the null set(i) Set of odd natural numbers divisible by 2(ii) Set of even prime numbers
(i) Because odd numbers are not divisible by two, a set of odd natural numbers divisible by two is a null set. (ii) Because 2 is an even prime number, the set of even prime numbers is not a null...
Which of the following are examples of the null set(i) x: x is a natural numbers, x 7(ii) y: y is a point common to any two parallel lines
(i) x: x is a natural integer, and the ranges x < 5 and x > 7 are null sets because a number cannot be both less than 5 and more than 7. (ii) y: A point that is shared by any two parallel...
Which of the following sets are finite or infinite(i) The set of months of a year(ii) 1, 2, 3 …
(i) Because there are 12 items in the set of months of a year, it is a finite set. (ii) Because it contains an unlimited amount of natural numbers, 1, 2, 3,... is an infinite set.
Which of the following sets are finite or infinite(i) {1, 2, 3 … 99, 100}(ii) The set of positive integers greater than 100
(i) The numbers 1 to 100 are finite, so 1, 2, 3,...99, 100 is a finite set. (ii) Because there are infinite integers after 100, the set of positive integers greater than 100 is unlimited as well.
Is the following set finite or infiniteThe set of prime numbers less than 99
Because prime numbers less than 99 are finite, the set of prime numbers less than 99 is finite as well.
State whether each of the following set is finite or infinite:(i) The set of numbers which are multiple of 5(ii) The set of animals living on the earth
(i) Because the multiples of 5 are infinite, the set of numbers that are multiples of 5 is unlimited. (ii) The number of animals living on the planet is finite, hence the set of animals living on...
State whether the following set is finite or infinite: The set of circles passing through the origin (0, 0)
Because an infinite number of circles can pass through the origin (0, 0), the set of circles travelling through the origin is endless.
In the following, state whether A = B or not:(i) A = {a, b, c, d}; B = {d, c, b, a}(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
(i) A = {a, b, c, d}; B = {d, c, b, a} The order in which a set's elements are listed has no bearing. Therefore, A = B. (ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18} We know that 12 ∈ A but 12 ∉ B....
In the following, state whether A = B or not:(i) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10}(ii) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30 …}
(i) A = {2, 4, 6, 8, 10}; B = {x: x is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10} So, A = B (ii) A = {x: x is a multiple of 10} B = {10, 15, 20, 25, 30 …} We know that 15 ∈ B but 15 ∉ A....
Are the following pair of sets equal? Give reasons.(i) A = {2, 3}; B = {x: x is solution of }(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
(i) A = {2, 3}; B = {x: x is solution of $x^{2}+5x+6=0$} $x^{2}+5x+6=0$ can be re-arranged as x(x + 3) + 2(x + 3) = 0 (x + 2) (x + 3) = 0 So, x = –2 or x = –3 Here A = {2, 3}; B = {–2, –3}...
From the sets given below, select equal sets:A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}, E = {–1, 1}, F = {0, a}, G = {1, –1}, H = {0, 1}
A = {2, 4, 8, 12}; B = {1, 2, 3, 4}; C = {4, 8, 12, 14} D = {3, 1, 4, 2}; E = {–1, 1}; F = {0, a} G = {1, –1}; H = {0, 1} We know, 8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H A ≠ B, A ≠ D, A ≠...
State whether each of the following set is finite or infinite:(i) The set of lines which are parallel to the x-axis(ii) The set of letters in the English alphabet
(i) The lines parallel to the x-axis are infinite. So the set of lines parallel to the x-axis is unlimited as well. (ii) Because the English alphabet comprises only 26 letters, it is a finite set.