Final answer:
The statement (R • B) ≡ (B ⊃ ¬ R) is self-contradictory because it implies that R must be both true and false at the same time, which is logically impossible. Hence, the correct answer is c. Self-contradictory.
Step-by-step explanation:
The logical statement provided is (R • B) ≡ (B ⊃ ¬ R), which is the equivalence between a conjunctive statement and a conditional statement. To determine whether this statement is logically equivalent, tautologous, self-contradictory, or contingent, we need to analyze its logical form and compare the truth values of both sides of the equivalence under various interpretations.
A universal statement such as 'All A are B' can be considered equivalent to a conditional 'If A, then B'. Similarly, our given statement compares a conjunction ('R and B') with a conditional expression ('If B, then not R'). Determining the logical relation involves assessing whether they can consistently hold true under the same conditions.
From logical analysis, we know that (R • B) implies both R and B are true. Yet, (B ⊃ ¬ R) implies that if B is true, then R must be false. These cannot be true at the same time, thus the statement creates a contradiction. It can also be considered self-contradictory because it contains conditions where R must be true and false simultaneously, which is an impossibility. Therefore, the correct choice is c. Self-contradictory.