Final answer:
The correct translation of the compound statement -(p \u2228 \u00ACq) is option b - It is not the case that students are happy or teachers are not happy, which aligns with the law of noncontradiction.
Step-by-step explanation:
The compound statement -(p \u2228 \u00ACq) can be translated into words by understanding the logical operators and their meanings. The symbol \u2228 represents 'or', \u00AC represents 'not', and the prefix - represents the negation of the entire statement enclosed within the parentheses.
Looking at the inner part of the compound statement p \u2228 \u00ACq, it says 'Students are happy (p) or Teachers are not happy (\u00ACq)'. The negation of this entire statement, indicated by the prefix -, tells us that it is not the case that this inner part of the statement is true. Therefore, the correct translation into words is 'It is not the case that students are happy or teachers are not happy', which corresponds to option b.
Option b is correct because it reflects the denial of the possibility that either students are happy or teachers are not happy. The negation turns the possibility into a negation of both parts: students being happy and teachers being not happy together. This is aligned with the law of noncontradiction, which states that a statement and its negation cannot both be true at the same time.