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7 pags., 4 figs., 2 tabs. -- Open Access funded by Creative Commons Atribution Licence 4.0 ; The quasi-free scattering reactions C(p,2p) and C(p,pn) have been studied in inverse kinematics at beam energies of 300–400 MeV/u at the RB-LAND setup. The outgoing proton-proton and proton-neutron pairs were detected in coincidence with the reaction fragments in kinematically complete measurements. The efficiency to detect these pairs has been obtained from GEANT4 simulations which were tested using the C(p,2p) and C(p,pn) reactions. Experimental cross sections and momentum distributions have been obtained and compared to DWIA calculations based on eikonal theory. The new results reported here are combined with previously published cross sections for quasi-free scattering from oxygen and nitrogen isotopes and together they enable a systematic study of the reduction of single-particle strength compared to predictions of the shell model over a wide neutron-to-proton asymmetry range. The combined reduction factors show a weak or no dependence on isospin asymmetry, in contrast to the strong dependency reported in nucleon-removal reactions induced by nuclear targets at lower energies. However, the reduction factors for (p,2p) are found to be 'significantly smaller than for (p,pn) reactions for all investigated nuclei. ; This work was supported by the German Federal Ministry of Education and Research (BMBF projects 05P2015RDFN1 and 05P15WOFNA), through the GSI-TU Darmstadt cooperation agreement, by the State of Hesse through the LOEWE center HIC for FAIR, and the Helmholtz-Gemeinschaft through the graduate school HGS-HIRe. This work was supported by the European Union by means of the European Commission within its Seventh Framework Program (FP7) via ENSAR (Contract No. 262010), and the Spanish CICYT research grants FPA2012-32443, FPA2015-64969-07387, and FPA2015-69640-C2-1-P. This work has supported by the Swedish Research Council under contract number 621-2011-5324. C.A.B. acknowledges support from the U.S. NSF grant No. 1415656 and the U.S. DOE grant No. DE-FG02-08ER41533. Supported by the Portuguese FCT under the project PTDC/FIS/ 103902/2008.