Truth Table

Date: 04/14/99 at 07:23:22
From: Sherri Pretorius
Subject: Discrete Mathematics - Baby set theory

I need help desperately with this one - I just keep getting it wrong.

Prove that (X(an upside down U)Y)' = X' u Y' without using a Venn 
diagram.    

Thanks,
Sherri

Date: 04/14/99 at 14:11:02
From: Doctor Anthony
Subject: Re: Discrete Mathematics - Baby set theory

You can use a truth table.

  (x and y) means INTERSECTION and you multiply
  (x or y)  means UNION and you add 

    x   y   x'   y'   (x and y)   (x and y)'   (x' or y') 
   -------------------------------------------------------
    0   0   1    1        0          1             1
    0   1   1    0        0          1             1
    1   0   0    1        0          1             1
    1   1   0    0        1          0             0
   -------------------------------------------------------

Comparing the last two columns we see that the two expressions are 
identical.  It follows that

     (x and y)' = x' or y'

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/