Which one of the following is an acceptable selection of representatives for the committee?

hales July 12, 2019

"Either Or"

I would love clarification on diagraming either/or questions - generally either or questions mean that at least one is present, possibly all. However, in the case of this example, with the wording "If either J or M is selected, the other must also be selected" - the condition is not treated as an either/or, but rather as a "both." (Diagramed as J <-->M). Is this because there is no option for J or M to NOT be present? The must always be present? So, even though there is the "either or" wording, we move straight to the option of "either or" that is if both are present?

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Ravi July 12, 2019

@hales,

Great question. We can treat the rule that says, "If either J or M is
selected, the other must also be selected" like it's saying "if and
only if," so this is why there's a double arrow.

J< - >M
/M< - >/J (contrapositive)

As seen by the contrapositive, there J and M don't have to be in. They
can also both be out. However, we know that either both of them are
in, or both of them are out. We'll never have a scenario where one of
them is in and the other is out.

Hope this helps. Let us know if you have any other questions!

Troy December 2, 2019

How were you guys able to conclude that this was an IN/OUT game? What are the keywords/ signifiers to determine what type of game it is?

shunhe January 7, 2020

Hey @Troy,

In this question, note that the housing committee will have 5 representatives, but we have a total of 9 possible selections. This means that no matter what, 4 people aren't going to be in the housing committee. That's how we know it's an in/out question! The size of the group is smaller than the total number of possible participants, and so some are going to have to be in, and some are going to have to be out. Hope this helps!

Yusuf-Adkins July 13, 2021

hello I am very confused with diagramming the last condition.

" M and J cannot both be selected" .. so that to me , I thought, was a "either or condition" . So I diagrammed it as

If not M than J
contropositive
If not J than M

So that would mean that one of M/J would be in the in collum not out collum.

Can you please explain