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### 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/
```
Associated Topics:
High School Sets

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