Final answer:
The question involves the breakdown of UENR Mathematics Department lecturers according to their teaching areas represented on a Venn diagram. At least 2 lecturers teach applied math and statistics, at least 3 teach only statistics, at least 5 teach at least two courses, and the number of lecturers teaching exactly one course can be inferred by accounting for all other lecturers.
Step-by-step explanation:
The UENR Mathematics Department has 12 lecturers, broken down into the following areas of teaching: 7 teach pure math, 6 teach applied math, and 5 teach statistics. However, some lecturers may teach in more than one area, and we have particular constraints to consider: 3 lecturers teach both pure and applied math, and no one teaches both pure math and statistics. To represent this information, we use a Venn diagram depicting three intersecting sets for pure math, applied math, and statistics.
Number of Lecturers Teaching Specific Combinations
- Applied math and statistics: Assuming no overlap with pure math and that each lecturer only teaches in one or two fields, we can deduce by elimination and given constraints that just two lecturers teach applied math and statistics.
- Only Statistics: Since we know five lecturers teach statistics, subtracting the two that teach both statistics and applied math leaves us with three lecturers who teach only statistics.
- At least two courses: We know at least three lecturers teach pure and applied math, and at least two more teach applied math and statistics, meaning at minimum five lecturers teach at least two courses.
- Exactly one course: By accounting for the total lecturers and those teaching multiple courses, we can find out the number who teach exactly one course.
To determine the exact numbers, further information would be needed to resolve any shared teaching roles between statistics and applied math that don't involve pure math. Without additional details, we can only provide estimates based on the provided constraints.