Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Sure, let's work through the problem step-by-step.
Given sets:
- [tex]\( A = \{36\} \)[/tex]
- [tex]\( B = \{1, 2, 3\} \)[/tex]
Let's find the Cartesian products [tex]\( A \times B \)[/tex] and [tex]\( B \times A \)[/tex].
### a) Cartesian Product [tex]\( A \times B \)[/tex]
The Cartesian product [tex]\( A \times B \)[/tex] is the set of all ordered pairs [tex]\((a, b)\)[/tex] where [tex]\( a \)[/tex] is an element of [tex]\( A \)[/tex] and [tex]\( b \)[/tex] is an element of [tex]\( B \)[/tex].
Since [tex]\( A \)[/tex] contains only one element, 36, we pair it with each of the elements of [tex]\( B \)[/tex]:
1. Pairing 36 (from [tex]\( A \)[/tex]) with 1 (from [tex]\( B \)[/tex]) gives us the ordered pair [tex]\((36, 1)\)[/tex].
2. Pairing 36 (from [tex]\( A \)[/tex]) with 2 (from [tex]\( B \)[/tex]) gives us the ordered pair [tex]\((36, 2)\)[/tex].
3. Pairing 36 (from [tex]\( A \)[/tex]) with 3 (from [tex]\( B \)[/tex]) gives us the ordered pair [tex]\((36, 3)\)[/tex].
Therefore,
[tex]\[ A \times B = \{ (36, 1), (36, 2), (36, 3) \} \][/tex]
### b) Cartesian Product [tex]\( B \times A \)[/tex]
The Cartesian product [tex]\( B \times A \)[/tex] is the set of all ordered pairs [tex]\((b, a)\)[/tex] where [tex]\( b \)[/tex] is an element of [tex]\( B \)[/tex] and [tex]\( a \)[/tex] is an element of [tex]\( A \)[/tex].
Since [tex]\( A \)[/tex] contains only one element, 36, we pair each element of [tex]\( B \)[/tex] with 36 from [tex]\( A \)[/tex]:
1. Pairing 1 (from [tex]\( B \)[/tex]) with 36 (from [tex]\( A \)[/tex]) gives us the ordered pair [tex]\((1, 36)\)[/tex].
2. Pairing 2 (from [tex]\( B \)[/tex]) with 36 (from [tex]\( A \)[/tex]) gives us the ordered pair [tex]\((2, 36)\)[/tex].
3. Pairing 3 (from [tex]\( B \)[/tex]) with 36 (from [tex]\( A \)[/tex]) gives us the ordered pair [tex]\((3, 36)\)[/tex].
Therefore,
[tex]\[ B \times A = \{ (1, 36), (2, 36), (3, 36) \} \][/tex]
### Representing on the Cartesian Plane:
For part a) [tex]\( A \times B \)[/tex]:
- Points on Cartesian Plane: (36, 1), (36, 2), (36, 3)
For part b) [tex]\( B \times A \)[/tex]:
- Points on Cartesian Plane: (1, 36), (2, 36), (3, 36)
These ordered pairs are the coordinates that will be plotted on the Cartesian plane for each respective product.
Given sets:
- [tex]\( A = \{36\} \)[/tex]
- [tex]\( B = \{1, 2, 3\} \)[/tex]
Let's find the Cartesian products [tex]\( A \times B \)[/tex] and [tex]\( B \times A \)[/tex].
### a) Cartesian Product [tex]\( A \times B \)[/tex]
The Cartesian product [tex]\( A \times B \)[/tex] is the set of all ordered pairs [tex]\((a, b)\)[/tex] where [tex]\( a \)[/tex] is an element of [tex]\( A \)[/tex] and [tex]\( b \)[/tex] is an element of [tex]\( B \)[/tex].
Since [tex]\( A \)[/tex] contains only one element, 36, we pair it with each of the elements of [tex]\( B \)[/tex]:
1. Pairing 36 (from [tex]\( A \)[/tex]) with 1 (from [tex]\( B \)[/tex]) gives us the ordered pair [tex]\((36, 1)\)[/tex].
2. Pairing 36 (from [tex]\( A \)[/tex]) with 2 (from [tex]\( B \)[/tex]) gives us the ordered pair [tex]\((36, 2)\)[/tex].
3. Pairing 36 (from [tex]\( A \)[/tex]) with 3 (from [tex]\( B \)[/tex]) gives us the ordered pair [tex]\((36, 3)\)[/tex].
Therefore,
[tex]\[ A \times B = \{ (36, 1), (36, 2), (36, 3) \} \][/tex]
### b) Cartesian Product [tex]\( B \times A \)[/tex]
The Cartesian product [tex]\( B \times A \)[/tex] is the set of all ordered pairs [tex]\((b, a)\)[/tex] where [tex]\( b \)[/tex] is an element of [tex]\( B \)[/tex] and [tex]\( a \)[/tex] is an element of [tex]\( A \)[/tex].
Since [tex]\( A \)[/tex] contains only one element, 36, we pair each element of [tex]\( B \)[/tex] with 36 from [tex]\( A \)[/tex]:
1. Pairing 1 (from [tex]\( B \)[/tex]) with 36 (from [tex]\( A \)[/tex]) gives us the ordered pair [tex]\((1, 36)\)[/tex].
2. Pairing 2 (from [tex]\( B \)[/tex]) with 36 (from [tex]\( A \)[/tex]) gives us the ordered pair [tex]\((2, 36)\)[/tex].
3. Pairing 3 (from [tex]\( B \)[/tex]) with 36 (from [tex]\( A \)[/tex]) gives us the ordered pair [tex]\((3, 36)\)[/tex].
Therefore,
[tex]\[ B \times A = \{ (1, 36), (2, 36), (3, 36) \} \][/tex]
### Representing on the Cartesian Plane:
For part a) [tex]\( A \times B \)[/tex]:
- Points on Cartesian Plane: (36, 1), (36, 2), (36, 3)
For part b) [tex]\( B \times A \)[/tex]:
- Points on Cartesian Plane: (1, 36), (2, 36), (3, 36)
These ordered pairs are the coordinates that will be plotted on the Cartesian plane for each respective product.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.