First, let's write out all of the rules and their contrapositives. #1: J(s) -> K(r) K(s) -> J(r) #2: J(r) -> O(s) O(r) -> J(s) #3: L(s) -> N(r) and P(r) N(s) or P(s) -> L(r) #4: N(r) -> O(r) O(s) -> N(s) #5: P(r) -> K(s) and O(s) K(r) or O(r) -> P(s)
Now, let's look at what must be true when we have K in S. This means that we want to look for any rules in which K(s) is our Sufficient condition.
The contrapositive of Rule #1 is the only place in which K(s) is our Sufficient condition. It tells us that K(s) -> J(r). So now we can place J in R and look for any rules in which J(r) is our Sufficient condition so that we can make more deductions.
Rule #2 is the only rule in which J(r) is our Sufficient condition. It tells us that J(r) -> O(s). So now we can place O in S and look for any rules in which O(s) is our Sufficient condition so that we can make more deductions.
The contrapositive of Rule #4 is the only place in which O(s) is our Sufficient condition. It tells us that O(s) -> N(s). So we can place N in S. This leads us to answer choice (B).
Does that make sense? Please let us know if you have any other questions!
