If H is assigned to exactly one committee, and if no committee has both F and M assigned to it, then it must be true ...

BenMingov May 7, 2020

Hi Marissa, thanks for the question

If H is used only once, that means that H is used only in Policy. Meaning that F and G must be placed in Quality and Sales.

Since G conflicts with L and L has yet to be placed. It cannot be G in both Quality and Sales. Additionally, since F conflicts with M in this scenario, it too cannot be placed in both Quality and Sales. This means we are left with G in either Quality or Sales and F in either Quality or Sales.

We can create two hypotheticals to show this.

H __ __
G __ G
F F K

OR


H __ __
G __ F
F G K

In the first scenario, we fill Sales with M to not conflict with F. Additionally, L in Quality to not conflict with G.

In the second scenario we fill Sales with L to not conflict with G. Additionally, M in Quality to not conflict with F.


H __ M
G L G
F F K

AND



H __ L
G M F
F G K

Lastly, the only available variable to fill both Qualities is K. Which is why it is used twice in both hypotheticals. I hope this helps!

rachelsilver July 11, 2020

Why is K the only available variable?

rachelsilver July 11, 2020

ohh I just read the other question's answers and see now that one person can't hold two positions on the same committee