When is a conjunction such as p · q true?

In logic, a conjunction such as $p·q$ is a compound proposition that is true if and only if both of its component propositions, $p$ and $q$, are true; it is false otherwise.12

This relationship is a fundamental aspect of Boolean algebra and propositional calculus, where the truth-value of the compound is determined by the truth-values of its components through the use of logical connectives. You can visualize this using a truth table, which maps every possible combination of truth-values for the components to the resulting truth-value of the conjunction.134