Tita Mustikawati Selayar
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Proposisi dalam Matematika: Pemahaman Tentang Negasi Konjungsi, dan Disjungsi dan Penerapan Operasi Logika dalam Analisis Matematika Prihaten Maskhuliah; Tita Mustikawati Selayar; Aulia Salsabila Putri
Algoritma : Jurnal Matematika, Ilmu pengetahuan Alam, Kebumian dan Angkasa Vol. 3 No. 5 (2025): Algoritma : Jurnal Matematika, Ilmu pengetahuan Alam, Kebumian dan Angkasa
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/algoritma.v3i5.744

Abstract

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.
Sistem Bilangan Bulat sebagai Dasar Teori Bilangan Prihaten Maskhuliah; Aulia Salsabila Putri; Dewi Mawaddah Rumaf; Tita Mustikawati Selayar; Alfaris Syahdan Nurpratama; Iman Bugis; Erna Bugis
JURNAL RISET RUMPUN MATEMATIKA DAN ILMU PENGETAHUAN ALAM Vol. 5 No. 2 (2026): Agustus : JURRIMIPA: Jurnal Riset Rumpun Matematika dan Ilmu Pengetahuan Alam
Publisher : Lembaga Pengembangan Kinerja Dosen

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55606/jurrimipa.v5i2.10061

Abstract

Integers are one of the fundamental concepts in number theory that serve as the foundation for studying various more complex mathematical topics. This article aims to describe the integer number system, including its definition, properties, and basic operations on integers. This article was written using a qualitative research method with a literature review approach, specifically through the examination of various books and scientific sources relevant to number theory. The results of the study indicate that the integer system consists of negative integers, zero, and positive integers, which possess the properties of closure, commutativity, associativity, distributivity, identity, and the inverse of addition. Furthermore, the operations of addition, subtraction, multiplication, and division of integers follow interrelated rules, thereby forming a consistent system for solving various mathematical problems. An understanding of the concepts, properties, and operations of integers is expected to serve as a strong foundation for studying number theory and to enhance a more comprehensive understanding of mathematical concepts.