Simplification is a straightforward rule of logical inference. It says that if P ^ Q is true, then P is true. The rule may be obvious, but it is useful.

By the same token, knowing P v Q allows you to conclude that Q is true. Like disjunctive syllogism before it, the above rule and commutativity would imply this. Again, though, check with your professor to see if he or she requires using commutativity or permits simplifying either side of the conjunction.