Which of the following relation is NOT a function ?

Options

A. f = { (x , x) | x `in` R }
B. `g = { ( x, 3) | x in R }`
C. `h = { (n , (1)/(n)) | n in I}`
D. `t = { (n, n^(2) ) | n in N } `

Answer

To determine which of the given relations is NOT a function, we need to analyze each option based on the definition of a function. A relation is a function if every input (or element from the domain) has exactly one output (or element from the codomain).

### Step-by-Step Solution:

1. **Analyze Option A**:
- The relation is given as \( f(x) = (x, x) \) where \( x \in \mathbb{R} \).
- This means for every real number \( x \), the output is the same as the input.
- Example: \( f(-1) = (-1, -1), f(1) = (1, 1), f(2) = (2, 2) \).
- Since every input has a unique output, this is a function.

2. **Analyze Option B**:
- The relation is given as \( g(x) = (x, 3) \) where \( x \in \mathbb{R} \).
- This means for every real number \( x \), the output is always 3.
- Example: \( g(-1) = (-1, 3), g(0) = (0, 3), g(2) = (2, 3) \).
- Again, every input has a unique output (which is 3), so this is also a function.

3. **Analyze Option C**:
- The relation is given as \( h(n) = (n, \frac{1}{n}) \) where \( n \) is an integer.
- If we consider \( n = 0 \), we get \( h(0) = (0, \frac{1}{0}) \).
- The value \( \frac{1}{0} \) is undefined, which means there is no output for the input 0.
- Since not every input has a unique output, this relation is NOT a function.

4. **Conclusion**:
- The relation that is NOT a function is option **C**.

### Final Answer:
The relation that is NOT a function is **option C**.