Question #1699

"Either Or"

Started by hales · started 2019-07-12 03:44 · last activity 2021-07-13 23:18 · 4 replies

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?

Replies

  1. Ravi · 2019-07-12 16:57

    @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!

  2. Troy · 2019-12-02 17:18

    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?

  3. shunhe · 2020-01-07 15:41

    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!

  4. Yusuf-Adkins · 2021-07-13 23:18

    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

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