Boolean Identity: (x + yx) = (x + y)(x + z) what is z

Question

In the boolean Identity:

(x + yx) = (x + y)(x + z)

Where does z come from and what does it mean?

I think there is a typo in the exercise - should be rather $(x + yz) = (x + y)(x + z).$ — user376343, Nov 05 '18 at 18:28
It would have to be a typo in my text book 'Computer System Architecture 3e' - Mano. See(https://imgur.com/Vg8XKdw) identity 14. I've seen the same identity elsewhere on the web too. — Alabaster, Nov 05 '18 at 18:58

score 0 · Answer 1 · answered Nov 05 '18 at 18:27

0

I think it should be $$X+YZ=(X+Y)(X+Z)$$. Please check your question once again. Or see the link

answered Nov 05 '18 at 18:27

jayant98

If you found this answer helpful, then please upvote this answer. – jayant98 Nov 05 '18 at 18:34
I added the image of the identity to a comment under my question. – Alabaster Nov 05 '18 at 19:10

score 0 · Answer 2 · answered Nov 05 '18 at 18:56

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$x=0, 1=>x^2=x=>$ $$ \\x+xy=x^2+xy=x(x+y)=(x+0)(x+y) $$ $=>z=0$

answered Nov 05 '18 at 18:56

Samvel Safaryan

2 Answers2