Wave-particle duality, as manifest in the two-slit experiment, provides perhaps the most vivid illustration of Bohr＇s complementarity principle : wave-like behaviour (interference) occurs only when the different possible paths a particle can take are indistinguishable, even in principle(1). The introduction of a which path (welcher Weg) detector for determining the actual path taken by the particle inevitably involved coupling the particle to a measuring environment, which in turn results in dephasing (suppression of interference). In other words, simultaneous observations of wave and particle behaviour is prohibited. Such a manifestation of the complementarity principle was demonstrated recently using a pair of correlated photons, with measurement of one photon being used to determine the path taken by the other and so prevent single-photon interference(2). Here we report the dephasing effects of a which-path detector on electrons traversing a double-path interferometer. We find that by varying the sensitivity of the detector we can affect the visibility of the oscillatory interference signal, thereby verifying the complementarity principle for fermions.