Results 1 to 3 of 3

Math Help - Truth table

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    3

    Truth table

    Use a truth table to show that (p->q)-> r and p->(q->r) are or are not logically equpvalent
    Last edited by mr fantastic; October 17th 2009 at 02:08 PM. Reason: Changed post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by zap1231 View Post
    Use a truth table to show that (p->q)-> r and p->(q->r) are or are not logically equpvalent

    No need for a whole talbe: when you give the value F to all p,q,r, you get in (p --> q) --> r the value F, whereas in p --> (q --> r) you get T.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,807
    Thanks
    697
    Hello, zap1231!

    Use a truth table to show that (p \to q) \to r and p \to (q\to r)
    are or are not logically equivalent

    . . \begin{array}{|c|c|c||}<br />
p & q & r \\ \hline<br />
T & T & T \\ T & T & F \\ T & F & T \\ T & F & F \\<br />
F & T & T \\ F & T & F \\ F & F & T \\ F & F & F\\ \hline & & \\ \end{array} <br />
\begin{array}{cccccc} [(p & \to & q) & \to & r] & \Longleftrightarrow \\ \hline<br />
T & T & T & T & T & T \\ T & T & T & F & F & T\\ T & F & F & T & T & T \\<br />
T & F & F & T & F & T \\ F & T & T & T & T & T \\ F & T & T & F & F & {\color{red}F} \\<br />
F & T & F & T & T & T \\ F & T & F & F & F & {\color{red}F} \\\hline 1 & 2 & 1 & 3 & 1 & 4<br />
\end{array} \begin{array}{ccccc} [p & \to & (q & \to & r)] \\ \hline<br />
T & T & T & T & T \\ T & F & T  & F & F \\ T & T & F & T & T \\<br />
T & T & F & T & F \\ F & T & T & T & T \\ F & T & T & F & F \\<br />
F & T & F & T & T \\ F & T & F & T & F \\ \hline 1 & 3 & 1 & 2 & 1 \end{array}<br />
    . . . . . . . . . . . . . . . . . . . . . . . {\color{blue}\uparrow}
    . . . . . . . . . . . . . . . . . . .not equivalent

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Truth Table help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 3rd 2010, 12:37 PM
  2. Truth Table
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: July 21st 2010, 09:59 AM
  3. Please help with truth table?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 26th 2010, 09:16 AM
  4. Truth table
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 20th 2010, 05:25 AM
  5. Truth Table
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 5th 2009, 10:24 AM

Search Tags


/mathhelpforum @mathhelpforum