Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's break down each set and list its elements in tabular form.
(a) [tex]\( A = \{ x : x \in \mathbb{W}, x \leq 5 \} \)[/tex]
- [tex]\( \mathbb{W} \)[/tex] denotes the set of whole numbers (0, 1, 2, 3, ...).
- The set [tex]\( A \)[/tex] consists of whole numbers [tex]\( x \)[/tex] such that [tex]\( x \leq 5 \)[/tex].
- Therefore, [tex]\( A = \{0, 1, 2, 3, 4, 5\} \)[/tex].
(b) [tex]\( B = \{ x : x \in \mathbb{W}, -3 < x < 3 \} \)[/tex]
- [tex]\( \mathbb{W} \)[/tex] denotes the set of whole numbers.
- The set [tex]\( B \)[/tex] consists of whole numbers [tex]\( x \)[/tex] such that [tex]\( -3 < x < 3 \)[/tex].
- Therefore, [tex]\( B = \{-2, -1, 0, 1, 2\} \)[/tex].
(c) [tex]\( C = \{ x : x \text{ is divisible by } 12 \} \)[/tex]
- The set [tex]\( C \)[/tex] includes numbers that are multiples of 12.
- Therefore, [tex]\( C = \{12, 24, 36, 48, 60, 72, 84, 96, 108, 120\} \)[/tex].
(d) [tex]\( D = \{ x : x = 3p, p \in \mathbb{W}, p \leq 3 \} \)[/tex]
- The set [tex]\( D \)[/tex] consists of values [tex]\( x \)[/tex] such that [tex]\( x = 3p \)[/tex] where [tex]\( p \)[/tex] is a whole number and [tex]\( p \leq 3 \)[/tex].
- Therefore, [tex]\( D = \{0, 3, 6, 9\} \)[/tex].
(e) [tex]\( E = \left\{ x : x = a^2, a \in \mathbb{N}, 3 < a < 7 \right\} \)[/tex]
- [tex]\( \mathbb{N} \)[/tex] denotes the set of natural numbers (1, 2, 3, ...).
- The set [tex]\( E \)[/tex] consists of squares of natural numbers [tex]\( a \)[/tex] such that [tex]\( 3 < a < 7 \)[/tex].
- Therefore, [tex]\( E = \{16, 25, 36\} \)[/tex].
(f) [tex]\( F = \{ x : x = \frac{n}{n+1}, n \in \mathbb{N} \text{ and } n \leq 4 \} \)[/tex]
- The set [tex]\( F \)[/tex] consists of values [tex]\( x \)[/tex] calculated as [tex]\( x = \frac{n}{n+1} \)[/tex] where [tex]\( n \)[/tex] is a natural number and [tex]\( n \leq 4 \)[/tex].
- Therefore, [tex]\( F = \{0.5, 0.6666666666666666, 0.75, 0.8\} \)[/tex].
(g) [tex]\( G = \{ x : x \in \mathbb{N}, 3x - 2 < 5 \} \)[/tex]
- The set [tex]\( G \)[/tex] consists of natural numbers [tex]\( x \)[/tex] such that [tex]\( 3x - 2 < 5 \)[/tex].
- Therefore, [tex]\( G = \{1, 2\} \)[/tex].
(h) [tex]\( J = \left\{ x : x \in \mathbb{N}, x^2 < 16 \right\} \)[/tex]
- The set [tex]\( J \)[/tex] consists of natural numbers [tex]\( x \)[/tex] such that [tex]\( x^2 < 16 \)[/tex].
- Therefore, [tex]\( J = \{1, 2, 3\} \)[/tex].
(i) [tex]\( K = \{ x : x \text{ is a prime number which is a divisor of 42} \} \)[/tex]
- The set [tex]\( K \)[/tex] consists of prime numbers that are divisors of 42.
- Therefore, [tex]\( K = \{2, 3, 7\} \)[/tex].
(j) [tex]\( H = \{ x : x \text{ is a 2-digit natural number such that the sum of its digits is } 10 \} \)[/tex]
- The set [tex]\( H \)[/tex] consists of two-digit natural numbers where the sum of the digits is 10. For example, [tex]\( 19, 28, 37, 46, 55, 64, 73, 82, 91 \)[/tex].
- Therefore, [tex]\( H = \{19, 28, 37, 46, 55, 64, 73, 82, 91\} \)[/tex].
(a) [tex]\( A = \{ x : x \in \mathbb{W}, x \leq 5 \} \)[/tex]
- [tex]\( \mathbb{W} \)[/tex] denotes the set of whole numbers (0, 1, 2, 3, ...).
- The set [tex]\( A \)[/tex] consists of whole numbers [tex]\( x \)[/tex] such that [tex]\( x \leq 5 \)[/tex].
- Therefore, [tex]\( A = \{0, 1, 2, 3, 4, 5\} \)[/tex].
(b) [tex]\( B = \{ x : x \in \mathbb{W}, -3 < x < 3 \} \)[/tex]
- [tex]\( \mathbb{W} \)[/tex] denotes the set of whole numbers.
- The set [tex]\( B \)[/tex] consists of whole numbers [tex]\( x \)[/tex] such that [tex]\( -3 < x < 3 \)[/tex].
- Therefore, [tex]\( B = \{-2, -1, 0, 1, 2\} \)[/tex].
(c) [tex]\( C = \{ x : x \text{ is divisible by } 12 \} \)[/tex]
- The set [tex]\( C \)[/tex] includes numbers that are multiples of 12.
- Therefore, [tex]\( C = \{12, 24, 36, 48, 60, 72, 84, 96, 108, 120\} \)[/tex].
(d) [tex]\( D = \{ x : x = 3p, p \in \mathbb{W}, p \leq 3 \} \)[/tex]
- The set [tex]\( D \)[/tex] consists of values [tex]\( x \)[/tex] such that [tex]\( x = 3p \)[/tex] where [tex]\( p \)[/tex] is a whole number and [tex]\( p \leq 3 \)[/tex].
- Therefore, [tex]\( D = \{0, 3, 6, 9\} \)[/tex].
(e) [tex]\( E = \left\{ x : x = a^2, a \in \mathbb{N}, 3 < a < 7 \right\} \)[/tex]
- [tex]\( \mathbb{N} \)[/tex] denotes the set of natural numbers (1, 2, 3, ...).
- The set [tex]\( E \)[/tex] consists of squares of natural numbers [tex]\( a \)[/tex] such that [tex]\( 3 < a < 7 \)[/tex].
- Therefore, [tex]\( E = \{16, 25, 36\} \)[/tex].
(f) [tex]\( F = \{ x : x = \frac{n}{n+1}, n \in \mathbb{N} \text{ and } n \leq 4 \} \)[/tex]
- The set [tex]\( F \)[/tex] consists of values [tex]\( x \)[/tex] calculated as [tex]\( x = \frac{n}{n+1} \)[/tex] where [tex]\( n \)[/tex] is a natural number and [tex]\( n \leq 4 \)[/tex].
- Therefore, [tex]\( F = \{0.5, 0.6666666666666666, 0.75, 0.8\} \)[/tex].
(g) [tex]\( G = \{ x : x \in \mathbb{N}, 3x - 2 < 5 \} \)[/tex]
- The set [tex]\( G \)[/tex] consists of natural numbers [tex]\( x \)[/tex] such that [tex]\( 3x - 2 < 5 \)[/tex].
- Therefore, [tex]\( G = \{1, 2\} \)[/tex].
(h) [tex]\( J = \left\{ x : x \in \mathbb{N}, x^2 < 16 \right\} \)[/tex]
- The set [tex]\( J \)[/tex] consists of natural numbers [tex]\( x \)[/tex] such that [tex]\( x^2 < 16 \)[/tex].
- Therefore, [tex]\( J = \{1, 2, 3\} \)[/tex].
(i) [tex]\( K = \{ x : x \text{ is a prime number which is a divisor of 42} \} \)[/tex]
- The set [tex]\( K \)[/tex] consists of prime numbers that are divisors of 42.
- Therefore, [tex]\( K = \{2, 3, 7\} \)[/tex].
(j) [tex]\( H = \{ x : x \text{ is a 2-digit natural number such that the sum of its digits is } 10 \} \)[/tex]
- The set [tex]\( H \)[/tex] consists of two-digit natural numbers where the sum of the digits is 10. For example, [tex]\( 19, 28, 37, 46, 55, 64, 73, 82, 91 \)[/tex].
- Therefore, [tex]\( H = \{19, 28, 37, 46, 55, 64, 73, 82, 91\} \)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
