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Quick Boolean Agebra Question

  • Thread starter ZeroPivot
  • Start date
  • #1
54
0

Homework Statement


xy + compliment(xy) = 1


Homework Equations





The Attempt at a Solution



is it true? because x+compliment(x) = 1

maybe its not true...
 

Answers and Replies

  • #2
CompuChip
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Homework Helper
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Yes. Take ##x + \overline{x} = 1## and rename x to a: ##a + \overline{a} = 1##.
Now set ##a = xy##.

Note, however, that ##\overline{xy} \neq \overline{x} \overline{y}##.
 
  • #3
54
0
Yes. Take ##x + \overline{x} = 1## and rename x to a: ##a + \overline{a} = 1##.
Now set ##a = xy##.

Note, however, that ##\overline{xy} \neq \overline{x} \overline{y}##.
what if x=1 and y=0 the xy=0 and compliment(xy)=0 then 0+0 != 1
 
  • #4
tiny-tim
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Hi ZeroPivot! :smile:

(guys, thanks for the compliments, but it's complements! :wink:)
what if x=1 and y=0 the xy=0 and compliment(xy)=0 …
No, complement(xy) = 1 :wink:
 
  • #5
54
0
Hi ZeroPivot! :smile:

(guys, thanks for the compliments, but it's complements! :wink:)


No, complement(xy) = 1 :wink:
i meant compliment(x)compliment(y) = 0

but thanks.
 
  • #6
tiny-tim
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Hi ZeroPivot! :smile:
xy + compliment(xy) = 1

is it true? because x+compliment(x) = 1

maybe its not true...
i meant compliment(x)compliment(y) = 0

but thanks.
So you meant, is ##xy + \bar{x}\bar{y} = 1## ?

No.
 
  • #7
CompuChip
Science Advisor
Homework Helper
4,302
47
Hi ZeroPivot! :smile:



So you meant, is ##xy + \bar{x}\bar{y} = 1## ?

No.
Because if it were, ##\overline{xy}## would equal ##\bar x \bar y##. In fact it equals ##\bar x + \bar y##.
 

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