Final answer:
The valid conclusion from the given premises is ~(N • ~C), which is option D. It states that not both N and not C can be true, aligning with the provided premises.
Step-by-step explanation:
The question is related to logical deduction in a mathematical or philosophical context. The student has provided a series of premises, and the task is to determine the valid conclusion. Given the premises:
- ~A v R: The negation of A or R
- ~(N • C): Neither N and C
- R⋙C: If R then C
- C⋙N: If C then N
We are asked to conclude A v C: A or C. The answer is not explicitly provided in the premises, so we need to use logical deductions to find a valid conclusion. Given that R⋙C and C⋙N, it can be deduced that R implies N through C (if R, then C; if C, then N; so if R, then N). However, we are given that ~(N • C), so N and C cannot both be true.
We can confirm that ~(N • ~C) is a valid conclusion by using the provided premises. It translates to 'not both N and not C', or in other words 'either not N or C', which corresponds to the given premises that N and C cannot both be true due to ~(N • C).