<![CDATA[Reasoning is a process of logical thinking. Proof is a series of logical arguments to show the truth of a statement. Reasoning is needed in proving a statement. The purpose of this study is to describe the deductive reasoning of Olympiad students in solving mathematical proofs based on field independent and field dependent cognitive styles. The indicators of deductive reasoning used are compiling evidence against the correctness of solutions, checking the validity of an argument, drawing conclusions from mathematical statements. This study uses a descriptive qualitative approach, located at MAN 2 Malang City. Subject selection based on field independent–field dependent cognitive style using the GEFT questionnaire, as many as four students. The research data were in the form of answer sheets and interview transcripts and were analyzed through triangulation methods. The results showed that field independent students were able to fulfill all indicators and construct proofs using mathematical induction and Gaussian proofs correctly. Meanwhile, field dependent students cannot fulfill all indicators, and in compiling evidence using mathematical induction, students go through n = k proof, so the structure of the evidence is incomplete. ABSTRAK Penalaran merupakan proses berpikir logis. Bukti merupakan rangkaian argumen logis untuk menunjukkan kebenaran suatu pernyataan. Penalaran diperlukan dalam membuktikan suatu pernyataan. Tujuan penelitian ini untuk mendeskripsikan penalaran deduktif siswa olimpiade dalam menyelesaikan pembuktian matematika berdasarkan gaya kognitif field independent maupun field dependent. Indikator penalaran deduktif yang digunakan yaitu menyusun bukti terhadap kebenaran solusi, memeriksa keshahihan suatu argumen, menarik kesimpulan dari pernyataan matematika. Penelitian ini menggunakan pendekatan kualitatif deskriptif, berlokasi di MAN 2 Kota Malang. Pemilihan subjek berdasarkan gaya kognitif field independent–field dependent menggunakan angket GEFT, sebanyak empat siswa. Data hasil penelitian berupa lembar jawaban dan transkip wawancara serta dianalisis melalui triangulasi metode. Hasil penelitian menunjukkan bahwa siswa field independent dapat memenuhi seluruh indikator dan menyusun pembuktian menggunakan induksi matematika maupun bukti Gauss dengan tepat. Sedangkan siswa field dependent tidak dapat memenuhi seluruh indikator, dan dalam menyusun bukti menggunakan induksi matematika, siswa melewati pembuktian n=k, sehingga susunan bukti tidak lengkap.]]>
