Boolean algebra

  • Thread starter Tony11235
  • Start date
  • #1
Tony11235
255
0
With [tex] x \oplus y [/tex] defined to be (here I'm using x' as the complement of x) xy'+x'y, prove [tex] x(y \oplus z) = xy \oplus xz [/tex]

I'm stuck. Any hint or help would be great.
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
Well, what have you done so far?

(I presume xy is the "and" operation, and x+y is the "or" operation?)
 
  • #3
Tony11235
255
0
Would a truth table work?
 
  • #4
David
Science Advisor
41
0
You can just expand out both expressions and see they are the same. You will need to use de Morgan's laws to turn the complement of a product into a sum of complements, however. That is the only tricky part.
 
  • #5
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
Have you done anything on this problem, or just sit and stared at it?
 
  • #6
Tony11235
255
0
Hurkyl said:
Have you done anything on this problem, or just sit and stared at it?

I expanded the right side, thought deeply about it, tried a few other moves, but came up short and had to turn it in unfinished. Oh well, one low homework score won't kill me.
 
  • #7
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
Well, if you had showed what you had done, maybe we could have pointed out the key step you were missing. Oh well. :frown:
 

Suggested for: Boolean algebra

  • Last Post
Replies
2
Views
815
Replies
2
Views
607
Replies
7
Views
349
Replies
3
Views
686
  • Last Post
Replies
1
Views
601
Replies
2
Views
996
Replies
6
Views
225
Replies
1
Views
878
Replies
5
Views
918
  • Last Post
Replies
4
Views
912
Top