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November 27, 2015
Posted by **Anonymous** on Sunday, September 28, 2008 at 10:01pm.

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.

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**drwls**, Monday, September 29, 2008 at 4:20am<<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.

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**David Q**, Monday, September 29, 2008 at 2:32pmPut 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.

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**Anonymous**, Monday, September 29, 2008 at 3:03pmMy reasoning is based on a truth table, does that change anything?

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**David Q**, Monday, September 29, 2008 at 3:22pmIt 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).

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**David Q**, Monday, September 29, 2008 at 3:28pmThis 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

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**Anonymous**, Monday, September 29, 2008 at 3:36pmOk. Thanks very much for all your help.

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