jenzy569 said:
2. The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 23 said they had taken physics, 47 said they had taken chemistry and 5 said they had taken both. Seven said they had taken neither. How many recent high school grads were surveyed?
Before we start, were you able to finish the problem that was discussed in your previous post? Congratulations listening to mmm's advice, but please ask one question per thread.
This is a badly worded problem because it is not completely clear what was asked in the survey. (You'll have to pardon me. I read many survey results, and to my frustration, the summaries were frequently very badly expressed. You had to read the actual questions and the responses and the cross-tabs to make any sense of the summary.) Were there two questions, namely "Did you take physics?" and "Did you take chemistry/", or three questions, namely "Did you take physics but not chemistry?" and "Did you take chemistry but not physics?" and "Did you take chemistry and physics?" However, I am going to assume that only two questions were asked because that makes for a shorter questionnaire. If that assumption is wrong, we are going to get the wrong answer, but that is the problem's fault, not ours.
Concept. In math and logic, "X or Y" means "X or Y or both." This is a "NON-EXCLUSIVE OR." It is often symbolized by "v." which stands for the Latin word "vel" meaning "non-exclusive or." Latin had a different word for an "exclusive or," namely "aut."
Given our assumption, this problem can be treated as a question about intersection and union of sets and cardinality of intersection and union.
A = the set of all women who responded to the survey
B = the set of women who took chemistry OR physics
C = the set of women who took NEITHER chemistry NOR physics
D = the set of women who took chemistry
E = the set of women who took physics
F = The set of women who took physics AND chemistry
Question time. Using the notation of intersection and union
A = ?
B = ?
