Let A ={a,b}, then number of one-one functions from A to A possible are :

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the number of one-one functions from set A to set A, where A = {a, b}, we can follow these steps:

### Step 1: Understand the Definition of One-One Function
A one-one function (or injective function) is a function where each element of the domain maps to a unique element in the codomain. This means no two different elements in the domain can map to the same element in the codomain.

### Step 2: Identify the Sets
We have the set A = {a, b}. The number of elements in set A is 2.

### Step 3: Count the Choices for Mapping Elements
For a one-one function from A to A:
- The first element (let's say 'a') can be mapped to any of the 2 elements in set A (either 'a' or 'b').
- After mapping the first element, we have to map the second element (let's say 'b'). Since the function is one-one, 'b' can only be mapped to the remaining element that hasn't been used yet.

### Step 4: Calculate the Total Number of One-One Functions
- For the first element 'a', we have 2 choices (it can go to either 'a' or 'b').
- For the second element 'b', we will have only 1 choice left (the one that hasn't been used).

Thus, the total number of one-one functions can be calculated as:
\[ \text{Total One-One Functions} = \text{Choices for first element} \times \text{Choices for second element} = 2 \times 1 = 2 \]

### Conclusion
Therefore, the number of one-one functions from set A to set A is **2**.

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