# Is confidence transitive in asociation rules?

Given a set of rule such as:
$A \rightarrow B$; $B \rightarrow C$; that satisfy minimum confidence in the context of apriori algorithm meaning: $$\text{Conf}(A \rightarrow B) \geq \text{min. confidence}$$ and $$\text{Conf}(B \rightarrow C) \geq \text{min. confidence}$$

Is it possible to state that $\text{Conf}(A \rightarrow C) \geq \text{min. confidence}$?

I believe it's not possible to assert the later given that the relation between $\text{Support}(A \rightarrow B)$ and $\text{Support}(B \rightarrow C)$ doesn't give any information about the $\text{Support}(A \rightarrow C)$

Does this make sense?

Note: it's just a book exercise I'm trying to solve(not homework!) Here is the chapter link, it's in page 405 exercise 3.
