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Math Help - Logical conclusion

  1. #1
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    Logical conclusion

    Hi, I have got a question here.

    Is the logical conclusion B → 'A, CA, C 'B correct? First I do not understand what the statement C 'B means exactly. I googled and it says it means 'B is provable from C but I still do not understand what this is meant. I created a truth table for A, B, C and B → 'A, CA. I do not know whether that helps? Maybe from the truth table I can get the answer? Any help is appreciated and thanks in advance!
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  2. #2
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    Quote Originally Posted by Keep View Post
    Is the logical conclusion B → 'A, CA, C 'B correct? First I do not understand what the statement C 'B means exactly. I googled and it says it means 'B is provable from C but I still do not understand what this is meant. I created a truth table for A, B, C and B → 'A, CA. I do not know whether that helps? Maybe from the truth table I can get the answer? Any help is appreciated and thanks in advance!
    Have you done any formal arguments other than with truth-tables?
    For example:
    1.~B\to A'
    2.~C\to A
    \underline{3.~~C~~}
    \therefore ~ B'
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  3. #3
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    Quote Originally Posted by Plato View Post
    Have you done any formal arguments other than with truth-tables?
    For example:
    1.~B\to A'
    2.~C\to A
    \underline{3.~~C~~}
    \therefore ~ B'
    Do you mean
    1. ~B\to A' = 'B or 'A
    2. ~C\to A = 'C or A
    3. I don't understand the writing itself.
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  4. #4
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    Quote Originally Posted by Keep View Post
    Do you mean
    1. ~B\to A' = 'B or 'A
    2. ~C\to A = 'C or A
    3. I don't understand the writing itself.
    In your text material what does 'B mean?
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  5. #5
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    Quote Originally Posted by Plato View Post
    In your text material what does 'B mean?
    It means not B
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  6. #6
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    Do you know the terms: Modus Ponens (M.P.), Modus Tollens (M.T.)?
    Do you know how to use them in formal arguments?
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  7. #7
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    Quote Originally Posted by Plato View Post
    Do you know the terms: Modus Ponens (M.P.), Modus Tollens (M.T.)?
    Do you know how to use them in formal arguments?
    Never heard of them, and we were never taught. Even these questions, we are just given, we are never taught. Apparently the assumption is that we have to look for answers from books, search in internet etc. and do it all by ourself or sth. like that. But yeah I really never heard that. For me, if it is possible to answer the question using Truth table, that would be really good for me as it is easier and simple for me to understand.
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  8. #8
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    Is it not possible to convert these into a boolean algebra with the usual operators and then solve it by truth table?
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