Final answer:
The correct inference that can be made is that K is false. This conclusion comes from analyzing the logical relationships of the implication K implies L and the biconditional K if and only if not L. The only consistent option that satisfies both statements is that K must be false, leading to the inference of C) K.
Step-by-step explanation:
The student asked about the inference that can be made if K ≣ ~L / ~(L • ~K) // K⊨L. This expression contains logical symbols and can be translated into English as follows: We have a biconditional K if and only if not L given not (L and not K), and also K implies L. To infer something from these statements, we need to break them down and understand the relationships between the symbols.
Firstly, the implication K implies L (K⊨L) means if K is true, then L must be true. By the definition of implication, if K is false, then the implication is still true regardless of the truth value of L. Secondly, the biconditional K if and only if not L (K ≣ ~L) means K is true if and only if L is false, and vice versa. From these two statements together, we can gather that K cannot be true, because that would make L true (from the implication), which contradicts the biconditional where L should be false if K is true.
Therefore, K must be false (~K). This satisfies the biconditional, as L can be true if K is false. It also satisfies the implication since if K is false the implication cannot be false (remember, if the antecedent is false, the entire implication is true). Consequently, the statement that can be inferred is K, which means the answer is C) K.