Disjunction introduction is the logic principle that, if A is true, then it's true that either A or B is true.
For example, if it's true that it's raining outside, it's trivially true that either it's raining outside, or my car is freshly waxed. Since a disjunction is true if at least one of the terms is true, and we know that one of the terms is true, the second term is irrelevant for determining the truth value of the disjunction.
Disjunction is a binary truth-function, the output of which is a sentence true if at least one of the input sentences (disjuncts) is true, and false otherwise.
q is the disjunction of p and q, and is pronounced as ‘pea vel queue’ or ‘pea vee queue’ or ‘pea or queue’.
In this case, p and q are the disjuncts of the disjunction.
The rule that covers the relation between conjunction and disjunction is simply this: The denial of a conjunction is equivalent to (equal to) a disjunction of the denials of the propositions.
And, the denial of a disjunction is equivalent to a conjunction of the denials of the propositions.
The rule is: An implication is equivalent to a disjunction consisting of the denial of the antecedent as one disjunct and the consequent of the implication as the other disjunct.
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