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Definition of their determiner from the Oxford Advanced American Dictionary

      

    their

     determiner
    determiner
    NAmE//ðər//
     
    , NAmE//ðɛr//
     
    (the possessive form of they)
     
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  1. 1of or belonging to them Their parties are always fun. Which is their house?
  2. 2used instead of his or her to refer to a person whose sex is not mentioned or not known If anyone calls, ask for their number so I can call them back.
See their in the Oxford Advanced Learner's Dictionary