# Math Help - Truth Tables

1. ## 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.

2. Hello, diakin9942!

Here's the second one . . .

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

Give a logical statement and complete a Truth table

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

. . $\begin{array}{|c|c|c||ccccccccccc}
a & b & c & [(b & \to & a) & \wedge & (c & \to & a)] & \to & [c & \to & b] \\ \hline \hline
T&T&T & T&T&T &T& T&T&T &T& T&T&T \\
T&T&F & T&F&T &T& F&T&T &T& F&T&T \\
T&F&T & F&T&T &T& T&T&T &F& T&F&F \\
T&F&F & F&T&T &T& F&T&T &T& F&T&F \\
F&T&T & T&F&F &F& T&F&F &T& T&T&T \\
F&T&F & T&F&F &F& F&T&F &T& F&T&T \\
F&F&T & F&T&F &F& T&F&F &T& T&F&F \\
F&F&F & F&T&F &F& F&T&F &T& F&T&F \\ \hline \end{array}$

. . . . . . . . . . $\begin{array}{cccccccccccc}1 & \;\;2 & \;\;1 & \;3 & \;1 & \;2 & \;\;1 & \;\;4 & \;\;1 & \;\,2 & \;\,1 \end{array}$

The argument is not valid.

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