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Math Help - Urget Please help for this Propositional Calculus

  1. #1
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    Urget Please help for this Propositional Calculus

    Translate the following English arguments into propositional calculus (PC) and decide, in PC, for each argument whether it is valid argument or not:

    (a)
    (i) If belief in God has scientific backing, then its rational.
    (ii)
    No conceivable scientific experiment could decide the issue of whether there is a God If belief in God has scientific backing, then some conceivable scientific

    Therefore we conclude:

    Belief in God isnt rational.

    (b) (i) Every event with finite probability eventually takes places.

    (ii If the world powers dont get rid of their nuclear weapons, then theres a finite probability that humanity will eventually destroy the world.

    (iii)
    If every event with finite probability eventually takes places and theres a finite probability that humanity will eventually destroy the world, then humanity will eventually destroy the world.

    Therefore we conclude:

    Either the world powers will get rid of their nuclear weapons, or humanity will eventually destroy the world.

    (c) (i) If materialism is true, then idealism is false.
    (ii) If idealism is true, then materialism is false.
    (iii) If mental events exist, then materialism is false.
    (iii) If the materialist thinks that his or her theory is true, then mental events
    exist.

    Therefore we conclude:

    If the materialist thinks that his or her theory is true, then idealism is true.
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  2. #2
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    I'm struggling a bit with the first one (God). You properly observed the conditional nature of the second (Nukes), but entirely overlooked the same in the first (God).

    The Second: Destroy the World OR Get Rid of Nukes

    The First: Belief in God is Irrational OR Conceive of an Experiment.

    In addition to this oversight, the premise is not quite right. It should read: "No conceivable scientific experiment could decide the issue of whether there is OR IS NOT a God "
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  3. #3
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    Question may be little twisted

    you can work out as per your correctness.
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  4. #4
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    Smile Few more questions

    if you can help me for these folowing question that will be great

    Question 2:

    (a) The logical binary operations NAND denoted by ­ and NOR denoted by are defined as follows:
    (P ­ Q) ~ (P ^ Q)
    (P Q) ~ (P v Q)

    where ~, ^ and v respectively denote the logical operations of negation, conjunction and disjunction. Express
    (i) (P ­ Q) and (P Q) R in terms of only
    (ii) (~ P Q) in terms of only ­

    (b) Obtain Principal Disjunctive Normal and Principal Conjunctive Normal Form for the formula:
    (P Q) (R S)

    where P, Q, R and S logical (Boolean) variables.

    (c)
    Determine the validity of the conclusion S P from the following three premises:
    ~ P v Q , ~ (Q P v ~ R) and ~ (R ~ S) (R v ~ S)


    Thanx in advance
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