The function P is defined as:
''To each person on the earth is assigned a date of birth''. Is this function one-one? Give reason.

Answer

To determine whether the function \( P \) defined as "to each person on the earth is assigned a date of birth" is one-one (injective), we need to analyze the definition of a one-one function.

### Step-by-Step Solution:

1. **Understanding a One-One Function**:
A function \( f: A \rightarrow B \) is called one-one (or injective) if for every \( x_1, x_2 \in A \), whenever \( f(x_1) = f(x_2) \), it must follow that \( x_1 = x_2 \). This means that no two different elements in the domain can map to the same element in the codomain.

2. **Identifying the Sets**:
In our case, let the set \( A \) represent all the people on Earth, and let the set \( B \) represent all possible dates of birth. Each person in set \( A \) is assigned a date from set \( B \).

3. **Analyzing the Function**:
Now, consider two different people, say Person 1 (e.g., Ram) and Person 2 (e.g., Mohan). If both were born on the same date, say November 25th, then we have:
\[ P(\text{Ram}) = \text{November 25th} \]
\[ P(\text{Mohan}) = \text{November 25th} \]
Here, \( P(\text{Ram}) = P(\text{Mohan}) \) but \( \text{Ram} \neq \text{Mohan} \).

4. **Conclusion**:
Since we can find at least two different people who share the same date of birth, it violates the condition for a one-one function. Therefore, the function \( P \) is **not one-one**.

### Final Answer:
The function \( P \) is not one-one because multiple people can share the same date of birth.

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