- Mon Feb 11, 2019 6:58 pm
Since your post was edited I'd like to respond again so the thread feels cohesive for any future student who may be stuck here, which considering this game, I'd say that's a likely scenario.
It looks like you're still stuck on the consequences of the first rule and its contrapositive, so I'm gonna take one more crack at cleaning it up and hopefully helping it all click!
I wrote in my first reply in this thread of a shortcut style diagram I personally use for a situation such as this within a grouping game, but for added emphasis I'll try again with an analogy to boot for further clarification.
Let's say that a rule says this: To be elected president, a candidate must either be a Democrat or a Republican, but not both.
This has a similar/identical structure to the rule in question here, which states: "If mathematics is offered, then either literature or sociology (but not both) is offered."
This means that to be president you must be one party or the other, and you cannot be both or zero of the two.
Conditionally, my shortcut would look like: P --> D/R, which to me signifies that if P is selected, exactly ONE of D or R must be selected. (I'd put the D/R in a box if I had a pencil rather than a keyboard to do so).
The contrapositive would look like: ~D/R --> ~P, which means that if someone is NOT exactly one of those conditions (either they are of neither party or somehow both) then that person could not possibly be president.
That implies that there is no deduction I can force about someone who I know is not a Democrat, just like there is nothing to deduce about not including Literature into the game. That person can either be a Republican and maybe still be president, or can be neither of the two. Similarly, in this game, knowing that L is not selected leaves the door open for both Math and Sociology to be selected, or neither of the two.
So, to make a long and hopefully helpful story short, ~L --> ~M is not a valid deduction, much like ~Democrat --> ~President would not be.
(Just to make sure it's clear, I don't have the function to strike out variables in this forum so I use (~) to symbolize 'NOT' )
Does that clear it up?