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Quick De Morgan's Law Question

ls_hopeful_2017ls_hopeful_2017 Member
edited April 2016 in Logic Games 111 karma
I was wondering if anyone could help me out here. Always had trouble understanding this concept.

1. Say I am negating [A and B]. I know this turns to [/A or /B]. Does this or mean that BOTH A and B are out? I know it means either A is out, or B is out but can both possibly be out?

2. Conversely, if I was negating [/A and /B], I know this becomes A or B. Does this or mean that BOTH A and B could possibly be in? I know it means either A is in, or B is in, but can both possibly be in?

Not entirely sure when the "inclusive" or applies or not. Thanks a lot guys!
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Comments

  • Accounts PlayableAccounts Playable Live Sage ⭐
    3107 karma
    "Or" in both cases is inclusive, so yes to both questions.

    1.) Both could be out
    2.) Both could be in
  • ls_hopeful_2017ls_hopeful_2017 Member
    111 karma
    @"Accounts Playable" Thank you so much for the help!
  • ls_hopeful_2017ls_hopeful_2017 Member
    111 karma
    @"Accounts Playable" Also, I'm assuming that the only time that "or" is not inclusive is when they specifically say "not both"? Is that a correct assumption? Or are there instances where they may not specify but the "or" is exclusive?
  • Accounts PlayableAccounts Playable Live Sage ⭐
    3107 karma
    Yes. Assume that "or" is inclusive unless explicitly stated otherwise (i.e. "not both").
  • ls_hopeful_2017ls_hopeful_2017 Member
    111 karma
    @"Accounts Playable" Got it. Thanks again!
  • quinnxzhangquinnxzhang Member
    611 karma
    To modify the answer you were given, sometimes the "or" is a de facto exclusive-or. For example, if a rule tells you that Molly finished first or fifth, you can interpret that to be an exclusive-or. This is because you know that Molly couldn't have finished both first and fifth.

    However, when it's possible for both disjuncts to be true, you should interpret the "or" as an inclusive-or unless otherwise stated.
  • runiggyrunruniggyrun Alum Inactive Sage Inactive ⭐
    2481 karma
    @7JRBG180 said:
    Also, I'm assuming that the only time that "or" is not inclusive is when they specifically say "not both"?
    This might be obvious, but the other instance where "or" is not inclusive is when either laws of nature or other rules/games setup preclude "both" from happening.
    A is in Paris or London (definitely not both)
    Game setup: There are no ties. A or B is third -->not both, because there are no ties.
  • ls_hopeful_2017ls_hopeful_2017 Member
    111 karma
    @runiggyrun @quinnxzhang Thanks for the help, guys! Really grateful how awesome this community is.
  • GSU HopefulGSU Hopeful Core ⭐
    1644 karma
    @quinnxzhang Great explanation.
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