Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Online

    15
    ReputationRep:
    https://cdn.discordapp.com/attachmen...45/unknown.png

    the entry on the table on the bottom left which states that p is false while q is true i don't understand why the statement p implies q is true, is true. I don't get it because if there's no info on q how can it be true? You can't know that p implies q is true automatically from the simple fact that no info is given on the truth of q "so thus it can't be false".


    I don't get it or is the automatic default for any "unknown" "tied" propositions always true?

    It's just like saying if i go for a run, then i do it on monday this is in the form P\Rightarrow Q because going for a run is a sufficient cause for doing it on monday however simply because it is monday does not mean that you will always go for a run

    now p is going for a run and q is of course on a monday

    so if p is false then you do not go for a run and if q is true then it's a monday

    then if you do not go for a run then it's a monday

    the truth of that statement that if you do not go for a run then it's monday can't be true because p is false. now i can understand int he table inthe link that if both a false such that the statement reads if you do not go for a run then it is not monday is defo true it makes sense and pretty much is true because if you are not running then it is not a monday. Bc running is a sufficient cause for it being a monday to if you reverse it and make it false then it makes sense.

    However determining whether the statement that if you don't run then it's monday can't possibly be true as for the day to be a monday the sufficient reason is that you go for a run. So then if you don't run then it ain't a monday. So how can that statement be true?

    I'm not sure i can think of any other way to put it but i can't seem to convince myself otherwise unless there's a fact that it's assumed that all "tied" statements that could be either true or false are all automatically true. It just doesn't make sense to me can someone explain?
    • Community Assistant
    Online

    20
    ReputationRep:
    It literally says it below that table.

    "While P is false, P => Q gives no information about the truth of Q so P => Q cannot be false".

    You can't infer anything about Q, so the proposition can't be false - therefore it must be true. This comes from the section above, which defines in this particular case P as a sufficient condition but not a necessary one. So P being true is sufficient for the proposition to be true - so when P is true then the proposition is true; but it's not necessary - so then if P is false, the truth of the proposition only depends on Q.

    Essentially, because it's only sufficient and not necessary, while P is true, P => Q is true. While P is false, P => Q is true, no matter the "value" of Q.
    • Thread Starter
    Online

    15
    ReputationRep:
    (Original post by artful_lounger)
    It literally says it below that table.

    "While P is false, P => Q gives no information about the truth of Q so P => Q cannot be false".

    You can't infer anything about Q, so the proposition can't be false - therefore it must be true. This comes from the section above, which defines in this particular case P as a sufficient condition but not a necessary one. So P being true is sufficient for the proposition to be true - so when P is true then the proposition is true; but it's not necessary - so then the truth of the proposition only depends on Q.
    so then in my example as long as it is monday then you run?

    anyway so p is sifficient for q but not necessary like you say so then q is the deciding factor as to whether the statement is true or not? so if q is true then no matter if p is true or not then the statement p implies q is true regardless?
    Online

    10
    ReputationRep:
    (Original post by will'o'wisp2)
    https://cdn.discordapp.com/attachmen...45/unknown.png

    the entry on the table on the bottom left which states that p is false while q is true i don't understand why the statement p implies q is true, is true. I don't get it because if there's no info on q how can it be true? You can't know that p implies q is true automatically from the simple fact that no info is given on the truth of q "so thus it can't be false".


    I don't get it or is the automatic default for any "unknown" "tied" propositions always true?

    It's just like saying if i go for a run, then i do it on monday this is in the form P\Rightarrow Q because going for a run is a sufficient cause for doing it on monday however simply because it is monday does not mean that you will always go for a run

    now p is going for a run and q is of course on a monday

    so if p is false then you do not go for a run and if q is true then it's a monday

    then if you do not go for a run then it's a monday

    the truth of that statement that if you do not go for a run then it's monday can't be true because p is false. now i can understand int he table inthe link that if both a false such that the statement reads if you do not go for a run then it is not monday is defo true it makes sense and pretty much is true because if you are not running then it is not a monday. Bc running is a sufficient cause for it being a monday to if you reverse it and make it false then it makes sense.

    However determining whether the statement that if you don't run then it's monday can't possibly be true as for the day to be a monday the sufficient reason is that you go for a run. So then if you don't run then it ain't a monday. So how can that statement be true?

    I'm not sure i can think of any other way to put it but i can't seem to convince myself otherwise unless there's a fact that it's assumed that all "tied" statements that could be either true or false are all automatically true. It just doesn't make sense to me can someone explain?
    The way I saw the material conditional symbol is that:

     A \Rightarrow B,

    I saw this as in effect one whole statement "If A happend, then B happens".
    Meaning if A happens, then B has to follow.

    e.g. "If it rains"  \Rightarrow "The grass is wet".
    Meaning if it rains, then the "grass being wet" has to happen.
    If it does rain AND after the grass is wet, then this satisfies the logical statement.

    --------------------------------------------------------------

    If A does not happen, then we do not care (and  A \Rightarrow B is vacously true.)

    We only care about the sequence of events, that if A happens, then B happens as well.

    If that is the case, then statement  A \Rightarrow B is satisfied.
    (Also means that A is a sufficient condition for B).

    I hope this clears it up a little. If there is an error then tell me. :-)
    • Community Assistant
    Online

    20
    ReputationRep:
    (Original post by will'o'wisp2)
    so then in my example as long as it is monday then you run?

    anyway so p is sifficient for q but not necessary like you say so then q is the deciding factor as to whether the statement is true or not? so if q is true then no matter if p is true or not then the statement p implies q is true regardless?
    For the second part, yes. You're essentially assuming the conclusion then.

    It's easier to think about the other way around - there are four "states" for it to be in, for each combination of true and false. We know P=>Q, so the only way that would NOT be true (if P is sufficient but not necessary), is if Q is false. Anything else goes.

    This is because for the case where P is true but Q is false - the proposition (P=>Q) is telling us that we have the sufficient condition for Q to be true - that P is true - but for some reason Q is false. This contradicts the proposition and so the proposition is false in that case.

    Your conclusion of your worded statement is correct, from what I can tell. It's phrased really confusingly and it's kind of the reason I dislike wordy problems in logic, because it just obscures the actual simplicity of it.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.