Answers: (i) (‘∈’ - belongs to, ‘∉’ - does not belong to) 0……A 0 ∈ A Because, the number 0 is included in the set A. (ii) (‘∈’ - belongs to, ‘∉’ - does not belong to) -2……A -2 ∉ A Because, the...
Answers: (i) (‘∈’ - belongs to, ‘∉’ - does not belong to) 12…..A 12 ∉ A Because, the number 12 is not included in the set A. (ii) (‘∈’ - belongs to, ‘∉’ - does not belong to) 9….A 9 ∈ A Because,...
Answers: (i) (‘∈’ - belongs to, ‘∉’ - does not belong to) 4..…A 4 ∈ A Because, the number 4 is included in the set A. (ii) (‘∈’ - belongs to, ‘∉’ - does not belong to) -4.…A -4 ∉ A Because, the...
Answers: (i) This collection is not a set. The word ‘most dangerous’ is not well defined in this collection. The collection of dangerous animals’ changes from one person to another. (ii) This...
Answers: (i) This collection is a set. The collection of all the questions in the chapter is in a definite quantity forming a set. (ii) This collection is a set. The collection of all months of a...
Answers: (i) This collection is not a set. The word ‘difficult’ is not well defined in this collection. As a topic might be hard for one person but not for another person. (ii) This collection is a...
Answers: (i) This collection is a set. The collection of all the girls in your class is a well-defined collection forming a set. (ii) This collection is not a set. The word ‘most’ is not well...
Answers: (i) This collection is a set. The collection of all-natural numbers less than 50 makes a set because it is a well-defined collection. (ii) This collection is not a set. The word ‘good’ in...
The well-defined collections are called as sets. Examples: The collection of the best Indian cricket players is not a set. Still, the collection of all the best players is set. Vowel collection in...
is a natural number and divisor of 6} (ii) {1, 3, 5, 7, 9} (d) { is a letter of the word MATHEMATICS}Solution: (i) Here the elements are letters of the word MATHEMATICS. As a result, (i) matches with (d). (ii) Here the elements are the odd natural numbers that are less than 10. As a result, (ii)...
is a prime number and a divisor of 6} (ii) {2, 3} (b) { is an odd natural number less than 10}Solution: (i) The elements of this set are divisors of 6 as well as natural number. As a result, (i) matches with (c). (ii) Here 2 and 3 are the prime numbers which are also the divisors of 6. As a...
is a month of a year not having 31 days} (ii) F = { is a consonant in the English alphabet which proceeds k}.Solution: (i) E = {$x: x$ is a month of a year not having 31 days} As a result the elements are E = {February, April, June, September, November} (ii) F = {$x: x$ is a consonant in the English...
is an integer, x2 ≤ 4} (ii) D = { is a letter in the word “LOYAL”}Solution: (i) $C =$ {$x: x$ is an integer, x2 ≤ 4} It is known to us that $(–1)2 = 1 ≤ 4$ ; $(–2)2 = 4 ≤ 4$ ; $(–3)2 = 9 > 4$ So here $02 = 0 ≤ 4$, $12 = 1 ≤ 4$, $22 = 4 ≤ 4$, $32 = 9 > 4$ As...
is an odd natural number} (ii) B = { is an integer, 
}Solution: (i) A = {$x: x$ is an odd natural number} So the elements are A = {1, 3, 5, 7, 9 …..} (ii) B = {$x: x$ is an integer, $-1/2 < x < 9/2$} It known to us that $– 1/2 = – 0.5$ and $9/2 =...
}Solution: (i) {$1, 4, 9 … 100$} It known to us that $1 = 1^2$, $4 = 2^2$, $9 = 3^2 …100 = 10^2$. As a result, the provided set {$1, 4, 9… 100$} can be re-written in the set-builder form as {$x: x =...
} (ii) {
}Solution: (i) {$5, 25, 125, 625$} It is known to us that $5 = 5^1$, $25 = 5^2$, $125 = 5^3$, and $625 = 5^4$. Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as...
} (ii) {
}Solution: (i) {$3, 6, 9, 12$} The provided set can be re-written in the set-builder form as {$x: x = 3n$, $n ∈ N$ and $1 ≤ n ≤ 4$} (ii) {$2, 4, 8, 16, 32$} We know that $2 = 2^1$, $4 = 2^2$, $8 =...
Solution: (i) E = The set of all letters in the word TRIGONOMETRY TRIGONOMETRY is a 12 letters word out of which T, R and O are repeated. As a result, the provided set can be written in the roster...
is a two-digit natural number such that the sum of its digits is 8} (ii) D = { is a prime number which is divisor of 60}.Solution: (i) C = {$x: x$ is a two-digit natural number such that the sum of its digits is 8} 17, 26, 35, 44, 53, 62, 71, and 80 are the only elements of the given set As a result, the provided set...
is an integer and 
}. (ii) B = { is a natural number less than 6}.Solution: (i) A = {$x: x$ is an integer and $–3 < x < 7$} –2, –1, 0, 1, 2, 3, 4, 5, and 6 are the only elements of the given set. As a result, the provided set can be written in the roster...
Solution: (i) 2 ∈ A (ii) 10 ∉ A
Solution: (i) 0 ∉ A (ii) 4 ∈ A
Solution: (i) 5 ∈ A (ii) 8 ∉ A
Solution: (i) A collection of most dangerous animals of the world cannot be considered as well-defined collection. Since the criteria to find the dangerousness of an animal can vary from one animal...
Solution: (i) The collection of all even integers can be considered as well-defined collection. Since an integer which belongs to this collection can be found by anyone. As a result, this collection...
Solution: (i) The collection of all natural numbers less than 100 can be considered as well-defined collection. Since one can find a number that belongs to this collection. As a result, this...
Solution: (i) A group of eleven of the world's best cricket batsmen is not a well-defined collection. Because the criteria used to determine a batsman's talent differ from person to person. As a...
Solution: (i) The collection of all months of the year that begin with the letter J can be considered as well-defined collection of objects. Because each month in the collection can be identified....