which of the following relations are functions from A={1,3,5,7,9} to B={1,2,3,4,5} `f={(1,3),(3,1),(5,3),(5,5),(1,4)}`

Explanation

To determine whether the relation \( f = \{(1,3), (3,1), (5,3), (5,5), (1,4)\} \) is a function from set \( A = \{1, 3, 5, 7, 9\} \) to set \( B = \{1, 2, 3, 4, 5\} \), we need to check the definition of a function.

### Step-by-Step Solution:

1. **Understanding the Definition of a Function**:
A relation \( f \) from set \( A \) to set \( B \) is a function if every element in \( A \) is associated with exactly one element in \( B \). This means that for every \( x \in A \), there should be a unique \( y \in B \) such that \( (x, y) \in f \).

2. **List the Pairs in the Relation**:
...