The primary objective of the brain is to collect information from the body via nervous system and then either process those information or store them. These stored information are basically known as memory. Over the years Electroencephalography (EEG) signals have been used quite efficiently to evaluate the cognitive state of brain. In this paper, we aim to study the cognitive functioning of the brain when a user memorizes and then recognizes an object from a list of similar ones. For this purpose, we have employed wavelet transform to extract the relevant features pertaining to the two mental activities and support vector machine to distinguish between the two states. The classification accuracy, thus obtained, is above 79% for all subjects. It is also inferred from this study that during memorization the signals from the frontal and temporal lobes are dominant and during recognition, signals from the frontal and parietal lobes are dominant.