In logic, conjunctions and disjunctions are logical
connectives that are used to combine two or more propositions into a single,
compound proposition. These connectives describe the relationships between the
constituent propositions in terms of their truth values.
- Conjunction:
A conjunction is a compound proposition formed by connecting two or more
propositions using the logical connective “and.” The conjunction
of propositions P and Q is denoted as P ∧ Q and is true if and only if
both P and Q are true. If either P or Q (or both) is false, then the
conjunction P ∧ Q is false. The truth table for a conjunction is
as follows:
- Disjunction:
A disjunction is a compound proposition formed by connecting two or more
propositions using the logical connective “or.” The disjunction
of propositions P and Q is denoted as P ∨ Q and is true if at least
one of P or Q is true (or both are true). The disjunction P ∨
Q is false only if both P and Q are false. The truth table for a
disjunction is as follows:
Conjunctions and disjunctions are essential tools in
propositional logic for creating more complex propositions and analyzing the
relationships between their constituent parts. They provide a way to express
multiple conditions or requirements and to reason about the combined truth
values of these conditions.