Correct Answer: E
Explanation:
The conditions “J and J are holding hands” and “L and L are holding hands” are naturally symbolized as JJ and LL, respectively. The condition “K and K are not holding hands” can be symbolized as K...K. [The symbol ~(KK) would also work well, but the symbol K...K is more descriptive because it shows the space between the Ks.] The condition “One of the Ls is at one end of the line, and one of the Ms is at the other end” can be symbolized as L=1st/last and M=1st/last. The diagram will consist of eight dashed lines numbered 1 through 8, from left to right:
JJ
LL
K ... K
L = First / Last
M = First / Last
No significant conditions can be derived from the given information, and no conditions can be placed on the diagram. So we attack the questions.
Place a J in position 2:
Then, from the condition JJ, the other J must be in position 3, since only L or M can be first.
Next, since the Ls must be together and one of them must be either first or last, they must be in positions 7 and 8. This in turn forces M to be first:
Next, from the condition K...K, we see that the Ks must be in positions 4 and 6, which in turn forces the other M into position 5. Thus our uniquely determined diagram is
The answer is (E).