1. กำหนดให้ $$ (8 x, 15)=(15+3 x,-5 y) $$ จงหาค่าของ $$ x-y, x-y= $$ $$ \qquad $$ 2. กำหนดให้ $$ A=\{1,3,5\}, B=\{3,6\} $$ จงหาค่าของ 2.1 $$ \mathrm{A} \times \mathrm{B}= $$ $$ \qquad $$ $$ 2.2 \mathrm{~B} \times \mathrm{A}= $$ $$ \qquad $$ $$ 2.3 \mathrm{~B} \times \mathrm{B}= $$ $$ \qquad $$ $$ 2.3 \mathrm{~A} \times \mathrm{A}= $$ $$ \qquad $$ 3. กำหนดให้ $$ A=\{1,3,5\}, B=\{3,6\} $$ จงเขียนความสัมพันธ์ $$ r $$ แบบแจกแจงสมาชิก $$ 3.1 r_{1}=\{(x, y) \in A \times B \mid y=x-2\} $$ $$ , \mathrm{r}_{1} \doteq $$ $$ \qquad $$ $$ 3.2 r_{2}=\{(x, y) \in A \times A \mid y

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UpStudy AI · Accepted Answer

Alright, I need to solve these mathematical problems step by step. Let's start with the first one.

**Problem 1:**
We have the equation $$ (8x, 15) = (15 + 3x, -5y) $$. I need to find the value of $$ x - y $$.

First, let's break down the equation into two separate equations since they are equal component-wise.

1. $$ 8x = 15 + 3x $$
2. $$ 15 = -5y $$

Starting with the first equation:
$$ 8x = 15 + 3x $$
Subtract $$ 3x $$ from both sides:
$$ 8x - 3x = 15 $$
$$ 5x = 15 $$
Divide both sides by 5:
$$ x = 3 $$

Now, let's solve the second equation:
$$ 15 = -5y $$
Divide both sides by -5:
$$ y = -3 $$

Now that I have $$ x = 3 $$ and $$ y = -3 $$, I can find $$ x - y $$:
$$ x - y = 3 - (-3) = 3 + 3 = 6 $$

So, $$ x - y = 6 $$.

**Problem 2:**
Given sets $$ A = \{1, 3, 5\} $$ and $$ B = \{3, 6\} $$, I need to find the Cartesian products and their intersections.

1. $$ A 	imes B $$
2. $$ B 	imes A $$
3. $$ B 	imes B $$
4. $$ A 	imes A $$

Let's compute each one:

1. $$ A 	imes B = \{(1,3), (1,6), (3,3), (3,6), (5,3), (5,6)\} $$

2. $$ B 	imes A = \{(3,1), (3,3), (3,5), (6,1), (6,3), (6,5)\} $$

3. $$ B 	imes B = \{(3,3), (3,6), (6,3), (6,6)\} $$

4. $$ A 	imes A = \{(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)\} $$

**Problem 3:**
Given sets $$ A = \{1, 3, 5\} $$ and $$ B = \{3, 6\} $$, I need to define the relations $$ r_1 $$ and $$ r_2 $$ as specified.

1. $$ r_1 = \{(x, y) \in A 	imes B \mid y = x - 2\} $$
2. $$ r_2 = \{(x, y) \in A 	imes A \mid y < x\} $$

Let's find each relation:

1. For $$ r_1 $$:
   - $$ x = 1 $$: $$ y = 1 - 2 = -1 $$ → Not in $$ B $$
   - $$ x = 3 $$: $$ y = 3 - 2 = 1 $$ → Not in $$ B $$
   - $$ x = 5 $$: $$ y = 5 - 2 = 3 $$ → In $$ B $$
   
   So, $$ r_1 = \{(5, 3)\} $$

2. For $$ r_2 $$:
   - $$ x = 1 $$: $$ y < 1 $$ → $$ y = 1 $$ (since $$ y $$ must be in $$ A $$)
   - $$ x = 3 $$: $$ y < 3 $$ → $$ y = 1 $$
   - $$ x = 5 $$: $$ y < 5 $$ → $$ y = 1 $$ or $$ y = 3 $$
   
   So, $$ r_2 = \{(1,1), (3,1), (5,1), (5,3)\} $$

1. $$ x - y = 6 $$ 2.1 $$ A 	imes B = \{(1,3), (1,6), (3,3), (3,6), (5,3), (5,6)\} $$ 2.2 $$ B 	imes A = \{(3,1), (3,3), (3,5), (6,1), (6,3), (6,5)\} $$ 2.3 $$ B 	imes B = \{(3,3), (3,6), (6,3), (6,6)\} $$ 2.4 $$ A 	imes A = \{(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)\} $$ 3.1 $$ r_1 = \{(5,3)\} $$ 3.2 $$ r_2 = \{(1,1), (3,1), (5,1), (5,3)\} $$

กำหนดให้ จงหาค่าของ

กำหนดให้ จงหาค่าของ
2.1

3. กำหนดให้ จงเขียนความสัมพันธ์ แบบแจกแจงสมาชิก

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กำหนดให้ จงหาค่าของ กำหนดให้ จงหาค่าของ 2.1 3. กำหนดให้ จงเขียนความสัมพันธ์ แบบแจกแจงสมาชิก