Classification of EEG signals is an important task in Brain Computer Interface (BCI) research. However, the large number of attributes of EEG data is regarded as a curse for classifiers. This paper aims at dimensionality reduction of EEG signals. We use rough set theory to reduce the dimensions of EEG data. In particular, we use discernibility matrix (DM) to compute an indispensable set of attributes of the data so that the attribute set is reduced before classification. We then use Naive Bayes (NB) classifier, Support Vector Machine (SVM) and Extreme Learning Machine (ELM) for classification of the EEG data containing only these attributes. We compare our method with the more popular Principal Component Analysis (PCA). We have used EEG dataset from BCI competition-II to perform the experiments. Accuracy, recall and precision are used as metrics to measure the performance of the classifiers with original dataset, PCA-reduced dataset and DM-reduced dataset. The classification results we obtained for the DM-reduced dataset are found to be as good as for the whole dataset without reduction and generally better than PCA-reduced dataset.