Given the set A, would it be correct to say that there are 4 subsets of A that have single element?

Given the set $A = \{ 0, 1, 2, 3 \}$, would it be correct to say that there are $4$ subsets of $A$ that have a single element?

This is a question from a math book I'm studying. The answer to that question according to this book is that yes, it would be correct to say that there are 4 subsets of A that have a single element. Which would be: {1}, {2}, {3} and {4}. However, I was in doubt because I thought that the empty set is a subset with a single element of any other set. So wouldn't it be correct to say that there are 5 subsets with a single element for set A or is the book correct?

The empty set, by definition, has no elements. (So it does not have a single element.)