prove that a function f = `{(x,2x+1) : x in N}` defined on the set of natural numbers NxxN is one - one function.

Explanation

To prove that the function \( f = \{(x, 2x + 1) : x \in \mathbb{N}\} \) is a one-one function, we need to show that if \( f(x_1) = f(x_2) \), then it must follow that \( x_1 = x_2 \).

### Step-by-step Solution:

1. **Define the Function**:
The function is defined as \( f(x) = 2x + 1 \) for \( x \in \mathbb{N} \).

2. **Assume \( f(x_1) = f(x_2) \)**:
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