Which courses Alicia takes is fully determined if she takes Russian and which one of the following?

Vennela on July 19 at 02:45PM

Why is A incorrect

if W is in then can't have S at 9am, so can't have P, so that takes out J (bc R is in), G (bc W is in) and P (bc W is in)...leaving R, W, M, S at 3pm. Isn't that the only possibility if W and R are in?

1 Reply

Skylar on July 19 at 06:06PM

@Vennela-Vellanki, happy to help!

The flaw in your logic is that we cannot conclude J is out because R is in.
Rule #1 tells us:
not R -> J
not J -> R
This rule says nothing about what happens when R is sufficient, so we cannot make assumptions.

Let's look at (A) again. We start with:
R W __ __ | __ __ __
- Rule #5 says that Alicia takes either G or W but not both. Since we already have her taking W, this means that G must be out.
- The contrapositive of Rule #3 is: W -> not S(9). So, since W is in, we know S(9) is out. However, notice that we still don't know if Alicia takes S(3) or not.
- The contrapositive of Rule #4 is: not S(9) -> not P. Therefore, P is also out.
- This is as many deductions as we can make. We are left with S(3), J, and M unplaced. We know from our setup that either J or M must fill our last out spot, but we have no way of deciphering which one of the two to place. This means that (A) would not fully determine the courses Alicia takes, so it is incorrect.

Does that make sense? Please let us know if you have any other questions!