# tautology help

• Nov 17th 2008, 08:28 AM
srk619
help
hi

can anyone help figure this out:
• Nov 17th 2008, 08:36 AM
Jhevon
Quote:

Originally Posted by srk619
hi

can anyone help figure this out:

Use a truth table to find out whether
((A ^ (A => B)) ^ (B => C) ) => C
is a tautology.

here is the (incomplete) truth table. can you finish it? if the last column has T in all its entries, then the statement in question is a tautology

$\begin{array}{|c|c|c|c|c|c|} \hline

A & B & C & A \implies B & B \implies C & \{ [(A \wedge (A \implies B)] \wedge (B \implies C) \} \implies C \\
\hline T & T & T & & & \\
\hline T & T & F & & & \\
\hline T & F & T & & & \\
\hline T & F & F & & & \\
\hline F & T & T & & & \\
\hline F & T & F & & & \\
\hline F & F & T & & & \\
\hline F & F & F & & & \\
\hline
\end{array}$
• Nov 17th 2008, 09:09 AM
srk619
i think i got it