If set A and B are defined as
`A = {(x,y)|y = 1/x, 0 ne x in R}, B = {(x,y)|y = -x , x in R,}`. Then

Options

A. `A nn B = A`
B. `A nn B = B`
C. `A nn B = phi`
D. `A uu B = A`

Explanation

To solve the problem, we need to analyze the sets A and B given in the question.

### Step 1: Define Set A
Set A is defined as:
\[ A = \{(x, y) | y = \frac{1}{x}, x \neq 0, x \in \mathbb{R}\} \]
This means that for every real number \( x \) (except zero), \( y \) is equal to \( \frac{1}{x} \).

### Step 2: Generate Points for Set A
Let's generate some points for Set A:
- If \( x = 1 \), then \( y = \frac{1}{1} = 1 \) → Point: (1, 1)
- If \( x = 2 \), then \( y = \frac{1}{2} = 0.5 \) → Point: (2, 0.5)
- If \( x = 3 \), then \( y = \frac{1}{3} \approx 0.33 \) → Point: (3, 0.33)
- If \( x = -1 \), then \( y = \frac{1}{-1} = -1 \) → Point: (-1, -1)
- If \( x = -2 \), then \( y = \frac{1}{-2} = -0.5 \) → Point: (-2, -0.5)

So, Set A can be represented as:
\[ A = \{(1, 1), (2, 0.5), (3, 0.33), (-1, -1), (-2, -0.5), \ldots\} \]

### Step 3: Define Set B
Set B is defined as:
\[ B = \{(x, y) | y = -x, x \in \mathbb{R}\} \]
This means that for every real number \( x \), \( y \) is equal to \(-x\).

### Step 4: Generate Points for Set B
Let's generate some points for Set B:
- If \( x = 1 \), then \( y = -1 \) → Point: (1, -1)
- If \( x = 2 \), then \( y = -2 \) → Point: (2, -2)
- If \( x = -1 \), then \( y = 1 \) → Point: (-1, 1)
- If \( x = 0 \), then \( y = 0 \) → Point: (0, 0)

So, Set B can be represented as:
\[ B = \{(1, -1), (2, -2), (-1, 1), (0, 0), \ldots\} \]

### Step 5: Find the Intersection of Sets A and B
To find the intersection \( A \cap B \), we need to determine if there are any points that satisfy both conditions:
1. From Set A: \( y = \frac{1}{x} \)
2. From Set B: \( y = -x \)

Setting these equal to each other:
\[ \frac{1}{x} = -x \]
Multiplying both sides by \( x \) (noting \( x \neq 0 \)):
\[ 1 = -x^2 \]
This leads to:
\[ x^2 = -1 \]
Since there are no real solutions to this equation, we conclude that:
\[ A \cap B = \emptyset \]

### Step 6: Find the Union of Sets A and B
The union of sets A and B is given by:
\[ A \cup B = A + B \]
Since there are no common elements in A and B, the union will simply be the combination of both sets.

### Conclusion
Thus, we can summarize:
- The intersection \( A \cap B = \emptyset \)
- The union \( A \cup B = A + B \)