Final answer:
The statement about the vertebrate olfactory system being able to distinguish thousands of odorants is true, due to the presence of numerous olfactory receptors that allow humans to detect a wide range of odors.
Step-by-step explanation:
The statement that the vertebrate olfactory system can distinguish thousands of odorants through labeled line processing is true. Humans have around 350 olfactory receptor subtypes that combine to detect about 10,000 different odors. Odorant molecules dissolve in the nasal mucosa and bind to their corresponding olfactory sensory cells, which then transmit signals to the main olfactory bulb and other brain regions, contributing to the perception of odors. Additionally, more recent research suggests humans may be able to distinguish a much higher number of unique odorant molecules, potentially in the trillions.