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Math Help - Logic Question

  1. #1
    dpb
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    Logic Question

    Hi. I couldn't solve my problem because it has two conditional logical propositions. The problem is:


    can anyone help me about this, thanks =)
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  2. #2
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    Hello, dpb!

    We're expected to know that: . a \to b is equivalent to  \sim a \vee b


    Find a logically equivalent proposition for:
    . . (p \vee q) \to (\sim p \to q)

    by first writing its contrapositive, and then applying DeMorgan's law
    and the equality for \sim(p \to q)

    They were trying to be helpful by outlining the steps we should follow,
    . . but I think they made it more confusing.
    I don't see the purpose of using the contrapositive here.
    . . I wouldn't have done it that way.
    Besides, the statement is a tautology . . .


    Contrapositive: . \sim(\sim p \,\to \,q) \to \sim(p \vee q)

    which gives us: . \sim(p \vee q) \,\to \,\sim(p \vee q)


    And this is a tautology: "a thing implies itself" ... which is always true.
    I don't know of any "logically equivalent proposition" we can write . . .

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  3. #3
    dpb
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    thanks =)
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