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Math Help - Tell whether each proposition is true, is false, or has unknown status at this time.

  1. #1
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    Tell whether each proposition is true, is false, or has unknown status at this time.

    p is true
    q is false
    r's status is unknown at this time

    Tell whether each proposition is true, is false, or has unknown status at this time.

    q --> r (I know this would be true because if the hypothesis is false, the truth value is always true)

    (p^r) <--> r (The textbook says the answer is true but how would I know this? All I know is that p is true, so if I don't know r it can be either true or false)

    (q or r) <--> r (The textbook says this is true but I don't get how. All I know is q is false)

    Please help
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  2. #2
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    Re: Tell whether each proposition is true, is false, or has unknown status at this ti

    Quote Originally Posted by kmjt View Post
    p is true
    q is false
    r's status is unknown at this time

    Tell whether each proposition is true, is false, or has unknown status at this time.
    q --> r (I know this would be true because if the hypothesis is false, the truth value is always true)
    (p^r) <--> r (The textbook says the answer is true but how would I know this? All I know is that p is true, so if I don't know r it can be either true or false)
    (q or r) <--> r (The textbook says this is true but I don't get how. All I know is q is false)
    p \wedge r \Leftrightarrow r ia always true because if r\equiv T both sides are true and if r\equiv F both sides are false.
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    Re: Tell whether each proposition is true, is false, or has unknown status at this ti

    Quote Originally Posted by Plato View Post
    p \wedge r \Leftrightarrow r ia always true because if r\equiv T both sides are true and if r\equiv F both sides are false.
    I do not quite understand
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  4. #4
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    Re: Tell whether each proposition is true, is false, or has unknown status at this ti

    Hello, kmjt!

    p\text{ is true.}
    q\text{ is false.}
    r\text{ is either true or false.}

    Tell whether each proposition is true, is false, or has unknown status at this time.

    q \to r
    I know this would be true because if the hypothesis is false, the truth value is always true.
    Right!


    (p\wedge r)\;\leftrightarrow\;r
    The textbook says the answer is true but how would I know this?
    All I know is that p is true, so if I don't know r, it can be either true or false.

    Since p is true, we have: . (T \wedge r)\;\leftrightarrow\;r

    If r is true, we have: . (T \wedge T) \leftrightarrow T \quad\Rightarrow\quad T \leftrightarrow T

    If r is false, we have: . (T \wedge F) \leftrightarrow F \quad\Rightarrow\quad F \leftrightarrow F




    (q \vee r) \leftrightarrow r
    The textbook says this is true but I don't get how. All I know is q is false

    Since q is false, we have: . (F \vee r) \;\leftrightarrow\; r

    If r is true, we have: . (F \vee T) \leftrightarrow T \quad\Rightarrow\quad T \leftrightarrow T

    If r is false, we have: . (F \vee F) \leftrightarrow F \quad\Rightarrow\quad F \leftrightarrow F
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