If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

Options

A. 720
B. 120
C. 0
D. None of these

Answer

To solve the problem of finding the number of one-one and onto mappings from set A to set B, we follow these steps:

### Step 1: Understand the Definitions
- A **one-one (injective)** function means that each element of set A maps to a unique element of set B.
- An **onto (surjective)** function means that every element of set B is mapped by at least one element of set A.

### Step 2: Analyze the Sizes of the Sets
- Set A contains 5 elements.
- Set B contains 6 elements.

### Step 3: Determine the Possibility of Onto Mapping
For a function to be onto, the number of elements in set A must be greater than or equal to the number of elements in set B. In this case:
- Number of elements in A (5) < Number of elements in B (6).

### Step 4: Conclusion on One-One and Onto Mappings
Since the number of elements in A is less than the number of elements in B, it is impossible to have an onto mapping from A to B. Therefore, it cannot be both one-one and onto.

### Step 5: Final Answer
The number of one-one and onto mappings from set A to set B is **0**.

### Summary
Thus, the final answer is:
- **Number of one-one and onto mappings = 0**