Proposisi dalam Matematika: Pemahaman Tentang Negasi Konjungsi, dan Disjungsi dan Penerapan Operasi Logika dalam Analisis Matematika
DOI:
https://doi.org/10.62383/algoritma.v3i5.744Keywords:
Conjunction, Disjunction, Mathematics, Negation, PropositionAbstract
This article examines the concept of propositions in mathematics, which are statements referred to as (closed sentences, false, values, and true values). The discussion covers negation, or what is known as negation, as operations that have truth values and truth tables. In addition, this article examines conjunction, or compound propositions that are true. (the combination of two questions), which involves two propositions with either true or false values. Furthermore, this article also examines disjunction, which involves statements containing conjunctionand also has truth tables. The primary objective is to provide a concise yet comprehensive understanding of propositions as logical and mathematical concepts. In addition, this article examines conjunction, or compound propositions that are true. A conjunction involves two propositions that are combined using the logical operator "and," symbolized by ∧. The conjunction of two propositions is true only when both individual propositions are true. For example, if P is true and Q is true, then the conjunction P ∧ Q is also true. However, if either P or Q is false, the conjunction P ∧ Q becomes false. The truth table for conjunction helps to clarify these conditions. Conjunction is often used in mathematical proofs, where multiple conditions must be satisfied simultaneously for a statement to hold true. Furthermore, this article also examines disjunction, which involves statements containing conjunction and also has truth tables. Disjunction, represented by the symbol ∨, involves two propositions and is true if at least one of the propositions is true. If both propositions are false, the disjunction is false. For instance, if P is false and Q is true, then P ∨ Q is true. The truth table for disjunction provides clarity on how this operation works. Disjunction is frequently used in mathematics and logic to express situations where at least one condition must be satisfied.
Downloads
References
Arifin, R., & Adi, M. (2022). Teori himpunan dan aplikasinya dalam matematika. Medan: Penerbit Pustaka.
Astuti, D., & Prasetyo, H. (2021). Teori himpunan dan aplikasinya dalam pembuktian matematika. Yogyakarta: UGM Press.
Bidala, A. (2022). Convers, invers, dan kontraposisi himpunan dan diagram Venn. https://doi.org/10.31219/osf.io/jdc4b
Damayanti, R. (2021). Logika matematika. Kediri: Pemeral Edukreatif.
Fahmi, S., & Priwantoro, W. S. (2021). Logika matematika dan himpunan. Yogyakarta: UAD Press.
Gardenia, Y., & Rahmawati, C. (2022). Logika matematika. Universitas Dirgantara Marsekal Suryadarma.
Hardi, T., & Rosyidi, M. (2022). Konsep dasar logika dan penerapannya dalam ilmu komputer. Malang: Penerbit Bumi Aksara.
Hasan, R., & Zulkarnain, M. (2018). Pembuktian dalam logika matematika. Bandung: Penerbit Alfabeta.
Isnaeni. (2022). Gabungan convers, invers, kontraposisi himpunan.
Iswarini, S. (2019). Skema pembuktian siswa dalam membuktikan proposisi matematika. Surabaya: Universitas Negeri Surabaya.
Kurniawan, A., & Wijaya, B. (2021). Matematika logika untuk pemula. Yogyakarta: Penerbit Intan Pariwara.
Linuhung, N., & Vahlia, I. (2017). Logika, himpunan, dan relasi dan fungsi. Pendidikan Matematika UM Metro.
Mangelep, N. (2009). Modul logika matematika.
Martono, N., & Shodiq, D. (2018). Dasar-dasar logika. Depok: PT Rajagrafindo Persada.
Nurjanah, I. (2017). Hubungan logika matematika dan bahasa.
Oktaviani, D., & Syamsul, A. (2022). Logika dalam teori sistem matematika. Surabaya: Universitas Negeri Surabaya.
Pradana, R., et al. (2024). Logika matematika. Universitas Budi Luhur.
Rahayu, P., & Fitriani, E. (2023). Teori logika matematika dalam analisis komputasi. Jakarta: Penerbit Mutiara.
Rahman, I., & Fitria, L. (2020). Pengenalan logika dan aljabar dalam matematika. Pekanbaru: Universitas Riau.
Resmawan. (2017). Pengantar logika matematika.
Rusli, M., Suniantara, P. K. I., & Nugroho, A. (n.d.). Logika & matematika. Yogyakarta: Andi.
Safitri, Y., & Fajri, M. (2020). Logika matematika dan teknik pembuktian. Semarang: Universitas Diponegoro.
Santoso, H., & Nugroho, R. (2020). Pemrograman logika matematika dalam rekayasa perangkat lunak. Surabaya: Penerbit Harapan.
Suciati, I., & Hajerina. (2023). Logika dan himpunan matematika. Gowa: CV Ruang Tentor.
Supriyadi, J., & Hadi, S. (2021). Pengantar logika dan teori set. Yogyakarta: Graha Ilmu.
Suryani, E., & Nugroho, M. (2019). Matematika logika untuk mahasiswa. Malang: Universitas Brawijaya.
Taufik, R., & Roni, E. (2018). Pembelajaran logika matematika berbasis teknologi informasi. Surabaya: Penerbit Insan Cendekia.
Unaidi, M. (2020). Penerapan logika matematika dalam kehidupan sehari-hari. Jakarta: Penerbit Aksara.
Yuniarti, F. A. D., & Prianggono, A. (2023). Logika matematika. Banyumas, Jawa Tengah: Wawasan Ilmu.
Zulfikar, M., & Hidayat, A. (2021). Penerapan logika matematika dalam teknik analisis. Jakarta: Penerbit Fajar.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Algoritma : Jurnal Matematika, Ilmu pengetahuan Alam, Kebumian dan Angkasa
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
