Ordered that the order of fact-finding and disposition is affirmed insofar as appealed from, without costs or disbursements.
The petitioner established by a preponderance of the evidence that the mother neglected the subject children because she knew or should have known that her boyfriend, who was frequently in the children's presence, physically abused the child Aliciya R., and because she failed to prevent further contact between Aliciya R. and the boyfriend once she became or should have become aware of the abuse ( see Family Ct Act § 1012 [f] [i] [B]; Matter of Cantina B., 26 AD3d 327, 328; Matter of Kanika M., 270 AD2d 490; Matter of Maxwell B., 269 AD2d 444, 445 [2000]; Matter of Commissioner of Social Servs. of City of N.Y. v Edyth W., 210 AD2d 328, 329). Moreover, in light of the mother's failure to exercise a minimum degree of care in providing Aliciya R. with proper supervision or guardianship, the petitioner also proved by a preponderance of the evidence that the mother derivatively neglected her younger child ( see Matter of Jose I., 13 AD3d 446, 447; Matter of Amanda RR., 293 AD2d 779, 781).