Final answer:
The correct answer to the question is 'a. authoritarian; permissive', linking a rigid parenting style with authoritarian and a lax parenting style with permissive.
Step-by-step explanation:
The question 'Among parenting styles, rigid is to ______ as lax is to ______.' can be answered by understanding that a 'rigid' parenting style correlates with the authoritarian approach, which is characterized by high demands and strict rules with little warmth or nurturing. In this parenting style, parents typically do not accommodate changes in rules, even for a vacation. On the other hand, a 'lax' parenting style corresponds with the permissive approach, in which parents impose few rules and demands, and often act more as a friend than a disciplinarian to their children. As a result, the correct answer to fill in the blanks would be: a. authoritarian; permissive.