Brain fog is a kind of mental problem, similar to chronic fatigue syndrome, and appears about 3 months after the infection with COVID-19 and lasts up to 9 months. The maximum magnitude of the third wave of COVID-19 in Poland was in April 2021. The research referred here aimed at carrying out the investigation comprising the electrophysiological analysis of the patients who suffered from COVID-19 and had symptoms of brain fog (sub-cohort A), suffered from COVID-19 and did not have symptoms of brain fog (sub-cohort B), and the control group that had no COVID-19 and no symptoms (sub-cohort C). The aim of this article was to examine whether there are differences in the brain cortical activity of these three sub-cohorts and, if possible differentiate and classify them using the machine-learning tools. he dense array electroencephalographic amplifier with 256 electrodes was used for recordings. The event-related potentials were chosen as we expected to find the differences in the patients' responses to three different mental tasks arranged in the experiments commonly known in experimental psychology: face recognition, digit span, and task switching. These potentials were plotted for all three patients' sub-cohorts and all three experiments. The cross-correlation method was used to find differences, and, in fact, such differences manifested themselves in the shape of event-related potentials on the cognitive electrodes. The discussion of such differences will be presented; however, an explanation of such differences would require the recruitment of a much larger cohort. In the classification problem, the avalanche analysis for feature extractions from the resting state signal and linear discriminant analysis for classification were used. The differences between sub-cohorts in such signals were expected to be found. Machine-learning tools were used, as finding the differences with eyes seemed impossible. Indeed, the A&B vs. C, B&C vs. A, A vs. B, A vs. C, and B vs. C classification tasks were performed, and the efficiency of around 60–70% was achieved. In future, probably there will be pandemics again due to the imbalance in the natural environment, resulting in the decreasing number of species, temperature increase, and climate change-generated migrations. The research can help to predict brain fog after the COVID-19 recovery and prepare the patients for better convalescence. Shortening the time of brain fog recovery will be beneficial not only for the patients but also for social conditions.