"all college students who drink beer make less than a 4.0 g. p.a. it is obvious then that drinking beer lowers a student's grades." this is an example of someone who believes that

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."