Final answer:
Option (2), EEG is the preferred method to obtain sub-second resolution of neural activity for cognitive tasks due to its non-invasive nature and real-time data capabilities.
Step-by-step explanation:
If you desire a non-invasive method with a short temporal resolution to track the changing neural environment for cognitive tasks, Electroencephalography (EEG) would be the preferred method to obtain sub-second resolution of neural activity. Unlike functional magnetic resonance imaging (fMRI), which provides detailed maps of neural activity with good spatial resolution but with a slower temporal resolution, EEG excels at detecting changes in brain activity directly through patterns of electrical activity on the scalp, providing real-time data.
Other mentioned methods such as Positron Emission Tomography (PET) and Magnetoencephalography (MEG) have their own advantages; PET gives a rough map of active brain areas but is invasive and has poor temporal resolution, whereas MEG offers data on the brain's magnetic field with better temporal resolution than fMRI, but is not as commonly used due to the difficulty of measurement.