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 cap B=A`
B. `A cup B=B`
C. `A cup B= phi`
D. `A cup B-A`

Explanation

To solve the problem, we need to analyze the sets A and B and determine their intersection and union.

### Step 1: Define the sets A and B
- Set A is defined as \( A = \{(x, y) | y = \frac{1}{x}, x \neq 0, x \in \mathbb{R}\} \).
- Set B is defined as \( B = \{(x, y) | y = -x, x \in \mathbb{R}\} \).

### Step 2: Find the intersection of sets A and B
To find the intersection \( A \cap B \), we need to find the 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 gives:
\[ \frac{1}{x} = -x \]

### Step 3: Solve the equation
Multiplying both sides by \( x \) (keeping in mind \( x \neq 0 \)):
\[ 1 = -x^2 \]
Rearranging this gives:
\[ x^2 = -1 \]

### Step 4: Analyze the result
The equation \( x^2 = -1 \) has no real solutions because the square of a real number cannot be negative. Therefore, there are no points that belong to both sets A and B.

### Step 5: Conclusion about the intersection
Since there are no common points, we conclude that:
\[ A \cap B = \emptyset \]

### Step 6: Analyze the union of sets A and B
The union \( A \cup B \) consists of all points that are in either set A or set B. Since there are no points in the intersection, the union is simply the combination of both sets.

### Final Result
- \( A \cap B = \emptyset \)
- \( A \cup B \) contains all points from both sets.