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Math Help - Truth Tables

  1. #1
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    Truth Tables

    I am confused on how to due to this problem
    (A). No A is B some of C is A. some C is not B

    (B). All B is A All C is A All C is B

    I need to give a logical statement and complete a Truth table

    This assignment is do tomorrow.
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  2. #2
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    Hello, diakin9942!

    Here's the second one . . .


    (B)\;\;\begin{array}{cc}& \text{All B is A.} \\<br />
& \text{All C is A.} \\ \hline<br />
\therefore & \text{All C is B.} \end{array}

    Give a logical statement and complete a Truth table

    In symbols: . \bigg[(b \to a) \wedge (c \to a)\bigg] \to \bigg[c \to b\bigg]


    . . \begin{array}{|c|c|c||ccccccccccc}<br />
a & b & c & [(b & \to & a) & \wedge & (c & \to & a)] & \to & [c & \to & b] \\ \hline \hline<br />
T&T&T & T&T&T &T& T&T&T &T& T&T&T \\<br />
T&T&F & T&F&T &T& F&T&T &T& F&T&T \\<br />
T&F&T & F&T&T &T& T&T&T &F& T&F&F \\<br />
T&F&F & F&T&T &T& F&T&T &T& F&T&F \\<br />
F&T&T & T&F&F &F& T&F&F &T& T&T&T \\<br />
F&T&F & T&F&F &F& F&T&F &T& F&T&T \\<br />
F&F&T & F&T&F &F& T&F&F &T& T&F&F \\<br />
F&F&F & F&T&F &F& F&T&F &T& F&T&F \\ \hline \end{array}
    . . . . . . . . . . \begin{array}{cccccccccccc}1 & \;\;2 & \;\;1 & \;3 & \;1 & \;2 & \;\;1 & \;\;4 & \;\;1 & \;\,2 & \;\,1 \end{array}


    The argument is not valid.

    . . There is an F in the last column (4).

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