Final answer:
The given statements ¬ (R ≡ M) and M • ¬ R are consistent because they can both be true at the same time, as the second statement fits within the possibilities allowed by the first.
The correct answer is D.
Step-by-step explanation:
The student's question involves determining the logical relationship between the two statements: ¬ (R ≡ M) and M • ¬ R. These statements refer to logical negation (not), logical biconditional (if and only if), and logical conjunction (and). To assess the relationship between these statements, we must first understand their meaning.
The first statement, ¬ (R ≡ M), asserts that R is not equivalent to M. In other words, R and M are not both true or both false at the same time. The second statement, M • ¬ R, suggests that M is true and R is false.
If we assess the truth values of both statements, we find that the first statement allows for four possibilities (R true and M false, R false and M true, both R and M true, or both false) but negates the case when R and M have the same truth value. The second statement sets a definite case where M is true and R is false. Since this scenario fits within the possibilities allowed by the first statement, the statements are consistent: they can both be true at the same time.
Therefore, the correct answer is d. Consistent. The statements are coherent as they do not contradict each other, referencing logical consistency and the idea that a set of beliefs is coherent if it's possible for them to be true simultaneously.