Theories in formal semantics state that the meanings of phrases and sentences are composed from the meanings of constituent parts and their syntactic mode of combination. Little is known about how composition is implemented in the brain. In two experiments, we studied on-line ERP and off-line behavioral responses to determiner-adjective-noun phrases. We assessed the effects of typicality and denotation, using intersective adjectives (typical: ‘A green turtle’ vs atypical: ‘An orange turtle’) or subsective adjectives (typical: ‘A slow turtle’ vs atypical: ‘A fast turtle’). After each phrase, participants had to respond to two questions (e.g., for ‘A fast turtle’: ‘Is it a common turtle?’; ‘Is it a fast animal?’) presented in random order. We contrasted these 4 semantic conditions, requiring composition, to 2 nonsemantic conditions, where the adjective was replaced with a pseudoword or a nonword. This contrast revealed a larger P600, if participants performed the task without explicit instructions and trial-to-trial feedback (experiment 1), or a larger sustained frontal negativity, if they were nudged to pay attention to meaning with instructions and feedback (experiment 2). The present dataset contains behavioural and EEG data from both experiments, as well as analysis scripts for both data types in R and Matlab/FieldTrip.