Math- repost

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This is a geometry question about disjunctions.
The symbol "v" represents "or". "~" stands for "negation of"
Here are two questions I need help with:
1. When p v ~q is false, then p is ______ and q is _____.
I think "false" belongs in both spaces.
2. When ~p v q is false, then p is ______ and q is ________.
I think "false" is the answer to both of these as well.
Am I correct?

Responses

Geometry - drwls, Sunday, September 28, 2008 at 8:19pm

Is this how geometry is taught these days? It looks like symbolic logic to me.

I believe the answers are:
1. false; true
2. true; false

However I am interpreting the v ("or") symbol as also meaning "and".

I don't see how you can logically convert an "or" statemen to an "and" statement as you have done

Geometry - Anonymous, Sunday, September 28, 2008 at 9:58pm

I am not converting them to "and" statements. I am breaking apart statements p and q individually. These are 'disjunctions', did you know that? I'm just trying to see if we're on the same page.

  • Math- repost -

    <<I am not converting them to "and" statements.>>

    It seems to me that you are. The first clause of each statement has p and q statements separated by a symbol you say represents "or". The second clause of the sentence contains an "and" between separate conclusions about p and q.

    I have reviewed the meaning of disjunction, and still believe your answers to both are wrong.

  • Math- repost -

    Put p = "Peter is a boy" and q = "Queenie is a girl". Then ~(p v ~q) means "It is not true that (either Peter is a boy or Queenie is a boy)". Doesn't that mean that both Peter is a girl and Queenie is a girl? If so, then p would be false and q would be true.

    Similarly, ~(~p v q) means "It is not true that (either Peter is a girl or Queenie is a girl)". That would presumably imply that both Peter is a boy and Queenie is a boy. If so, then p would be true and q would be false.

    In both instances you're effectively saying "If it isn't the case that at least one of A and B is true, then both of them must be false". (In the first instance, A=p and B=~q, whereas in the second instance, A=~p and B=q.)

    I'm not absolutely certain my reasoning is correct here, but I think it is.

  • Math- repost -

    My reasoning is based on a truth table, does that change anything?

  • Math- repost -

    It ought not to: a truth table should deliver the same answers. I've just had a go at doing the first one that way, and got the following (these columns probably won't line up, but you should be able to work out which heading relates to which column):

    P Q ~P ~Q (Pv(~Q)) ~(Pv(~Q)) (~P)^Q
    T T F F T F F
    T F F T T F F
    F T T F F T T
    F F T T T F F

    This gives me the answer I got earlier (i.e. the last two columns are the same).

  • Math- repost -

    This might be easier to read - just ignore the underscores:

    P_Q_~P_~Q_(Pv(~Q))__~(Pv(~Q)) __(~P)^(Q)
    T_T__F__F______T__________F__________F
    T_F__F__T______T__________F__________F
    F_T__T__F______F__________T__________T
    F_F__T__T______T__________F__________F

  • Math- repost -

    Ok. Thanks very much for all your help.

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