"For every line L and for every point P not lying on a given line L, there exists a unique line m passing through P and parallel to L" is known as playfair 's axiom.

Explanation

To determine whether the statement "For every line L and for every point P not lying on a given line L, there exists a unique line m passing through P and parallel to L" is true or false, we will analyze it step by step.

### Step-by-Step Solution:

1. **Understanding the Statement**:
The statement refers to a situation involving a line \( L \) and a point \( P \) that does not lie on line \( L \). It claims that there is a unique line \( m \) that can be drawn through point \( P \) that is parallel to line \( L \).

2. **Identifying the Axiom**:
This statement is a restatement of Playfair's Axiom, which is a version of Euclid's fifth postulate. Playfair's Axiom asserts that through a point not on a given line, there is exactly one line that can be drawn parallel to the given line.

3. **Analyzing the Conditions**:
- We have a line \( L \).
- We have a point \( P \) that is not on line \( L \).
- The statement claims the existence of a unique line \( m \) through \( P \) that is parallel to \( L \).

4. **Applying Playfair's Axiom**:
According to Playfair's Axiom, since point \( P \) is not on line \( L \), there indeed exists a unique line \( m \) that can be drawn through \( P \) that is parallel to line \( L \).

5. **Conclusion**:
Since the statement aligns perfectly with Playfair's Axiom, we conclude that the statement is **true**.

### Final Answer:
The statement is **true**.