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Math Help - Doubt about logic

  1. #1
    MHF Contributor arbolis's Avatar
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    Doubt about logic

    Hi,
    I've a doubt about his : True or false? : If \det AB=0 then A or B is not invertible.
    I know that \det A=0 or \det B=0 but there is also the possible case \det A and \det B=0. So I'm tempted to answer False.
    Because they say \{ \text{a proposition} \} \lor \{ \text{another proposition} \} while the answer could be \{ \text{a proposition} \} \land \{ \text{another proposition} \}. So does the \lor include the \land case?
    I know I don't explain myself well. You can answer the question true or false and I will understand. Thank you very much.
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  2. #2
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    There is a theorem: \left| {AB} \right| = \left| A \right|\left| B \right|.
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  3. #3
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by Plato View Post
    There is a theorem: \left| {AB} \right| = \left| A \right|\left| B \right|.
    Yes I know! ahahah. Sorry, I wasn't clear AT ALL.
    My answer would be that if \det AB=0, then or \det A=0 or \det B=0 or \det A and \det B=0.
    It's exactly the same as this case : (a-b)(z-y)=0. We have that or (a-b)=0 or (z-y)=0. But what I'm trying to say is that there is also the case " (a-b)=0 and (z-y)=0 ".
    I'm not sure I'm explaining well. That's why I'd like you or whoever who is sure and certain, to answer the "true or false" question. For me it would be false, because there could be the case and which is not included in the phrase "det A=0 or det B=0", which I interpret as "it's either det A=0 or det B=0, but not both at the same time". So basically I'm asking if I'm not interpreting things badly.
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    A OR B mean at least one of A or B is true maybe both.
    Does that help?
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  5. #5
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by Plato View Post
    A OR B mean at least one of A or B is true maybe both.
    Does that help?
    Yes it helps. Thank you infinitely! It means that the answer to the "True or false" is true.
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