Struggling with sorting games

[ripple]

I am having trouble grasping the basics of sorting games:

The Watsonville High School girls’ tennis team has eight players: Anita, Brody, Dawn, Elise,
Hannah, Ivana, Jeanine, and Martha. The coach needs to choose four players as junior
coaches for the elementary school team:

If she chooses Hannah, then she also chooses Martha.
She chooses Elise if and only if she doesn’t choose Ivana.
She chooses either Anita or Dawn, or both of them.
If she chooses Brody, then she doesn’t choose Martha.

I express the clues as follows:
H --> M
E/I
A or D or AD
B/M

The author of the book states that it helps to condense the formula to thus:

H --> M --> _B (I get this)
B --> _M --> _H (I don't get this)

There is nothing in the clues to suggest -M --> -H. I am confused. H --> M but no where does it say the inverse is true. I was working through one of the questions asking for a 'could be' list of members for the team, and the correct answer was a list of team members with H, but no M. I am totally confused. Help?

[maryadkins]

Here is how I would notate these rules:

If she chooses Hannah, then she also chooses Martha.

H --> M
-M --> -H

She chooses Elise if and only if she doesn’t choose Ivana.

A biconditional!

E --> -I
I --> -E
-I--> E
-E--> I

She chooses either Anita or Dawn, or both of them.

A/D or both

If she chooses Brody, then she doesn’t choose Martha.

B --> -M
M --> -B

B --> -M --> -H combines the last rule with the contrapositive of the first rule. If you're not sure what I mean by contrapositive, check out chapter 8 of the LR Strategy Guide or read up on it elsewhere! It's something you definitely want to know.

[ripple]

Thanks for that. I ended up figuring it out and have a much stronger grasp on contrapositives now. But now I am getting stumped on Subgroups Selection Games.

Five books are selected for a syllabus from three history books (A, B, and C), four philosophy books (D, E, F, and
G), and two literature books (H and I). At least one of each kind is selected, according to the following conditions:
If more than one philosophy book is chosen, both literature books are chosen.
If D is chosen, I is not chosen.
Either C or B must be chosen.
If B is chosen, then either D or F (or both) must be chosen.

I express the conditions as thus:

2+p -> H and I ( -I or -H -> 1p)
D -> -I (I -> -D)
C or B or CB
B -> D or F or DF (-D and -F -> -B)

I draw a scenario diagram for the first condition

---------B/C---H---I
p----p----h----l----l

Once I get past the 'test the rules' question, I get stuck. So for the following question, I just don't seem to know how to even being to diagram my way to the answer:

If book E is selected, then which one of the following
cannot be true?
a. H and I are both selected.
b. B and G are both selected.
c. B and H are both selected.
d. A and C are both selected.
e. C and G are both selected.

I am not sure why I am having such problem with this. Maybe I am not chaining conditions more where appropriate...just don't know.

[tommywallach]

Hey Ripple,

Is this from an official test? If so, could you please post about it in the relevant forum. Usually, this forum is more about general issues than just particular games that folks want advice on.

Thanks!

-t