During the 1980s the homicide rate in Britain rose by 50 percent. The

this question is most easily answered through process of elimination. (A)-(D) can be eliminated for logical reasons.

Between the wording of your question and the wording of the argument and answer choice, I'm a bit confused. Thus, let me just point out a couple of things that I think are relevant and you can tell me if I've answered your question, ok?

First of all, what you have listed as "C:" below is not quite right. It's not that rates of homicide are increasing, it's that rates of "unpremeditated assaults" are increasing. So an analysis of the argument looks more like this:

P: In the 80s, homicide rate rose 50%
P: Weapon usually a knife
P: Potentially lethal knives sold all around
P: Most homicides due to unpremeditated assaults within family
P: Even if such assaults increasing, probly no death if potentially lethal knives weren't around

C: Govt's fault for permitting potentially lethal knives to be sold

This is a complicated, and bad argument. The "even if... probably" statement is confusing, etc. The first four answer choices attempt to use smoke and mirrors to get you tangled up in the logic of all the premises.

(E) cuts right to the chase -- dealing directly with the rise of homicides in the 80s, and the family nature of the problem. If "potentially lethal knives" are household knives, these have always been available, so the rise in the 80s, therefore, can't be explained by this. If "potentially lethal knives" are actual weapons, these aren't in households!

This seriously weakens the central argument.