Results 1 to 5 of 5

Math Help - Using DeMorgan's Law, write an expression for the complement of F

  1. #1
    Junior Member
    Joined
    Apr 2013
    From
    USA
    Posts
    69
    Thanks
    1

    Using DeMorgan's Law, write an expression for the complement of F

    Using DeMorgan's Law, write an expression for the complement of F if F(x,y,z)= xy + x'z + yz'

    I know this property:

    (x'y') = (x' + y') and (x' + y') = x'y'

    But there's only one variable that is NOT'ed at a time, (x in the x'z and y in yz').
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Using DeMorgan's Law, write an expression for the complement of F

    Quote Originally Posted by lamentofking View Post
    I know this property:

    (x'y') = (x' + y') and (x' + y') = x'y'
    No, it's (xy)' = (x' + y') and (x + y)' = x'y'. The left-hand side is the negation of a conjunction or a disjunction.

    Quote Originally Posted by lamentofking View Post
    But there's only one variable that is NOT'ed at a time, (x in the x'z and y in yz').
    You don't need to transform F(x,y,z); you need to transform its negation. F is a sum (disjunction), so it's negation can be rewritten by De Morgan's law.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Aug 2010
    Posts
    961
    Thanks
    98

    Re: Using DeMorgan's Law, write an expression for the complement of F

    To begin with, emakarov solved the problem.

    I was curious about what it was about, so,

    P^Q: (and), PvQ: (or) have truth table definitions for P,Q True or False.

    T=F and F =T by definition.

    From the truth table definitions:

    (P^Q)=PvQ'
    (PvQ)=P^Q

    By definition, in this context, is ^ and + is v

    Reference wiki DeMorgans Laws
    Last edited by Hartlw; September 24th 2013 at 08:15 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2013
    From
    USA
    Posts
    69
    Thanks
    1

    Re: Using DeMorgan's Law, write an expression for the complement of F

    So if I negate F then F'(x,y,z)= (xy)' + xz' + y'z ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Using DeMorgan's Law, write an expression for the complement of F

    No, (xy + x'z + yz')' = (xy)'(x'z)'(yz')' = (x' + y')(x'' + z')(y' + z'') = (x' + y')(x + z')(y' + z).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: October 6th 2011, 02:48 PM
  2. re-write expression with abs value
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 6th 2010, 07:07 PM
  3. write log as an expression
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 8th 2009, 06:27 PM
  4. how can write this expression in z=x+yi
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 31st 2009, 01:20 AM
  5. Write the expression
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 10th 2006, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum