A postulate of boolean algebra: x+(y.z) = (x+y).(x+z)

[jackson6612]

x+(y.z) = (x+y).(x+z)

I don't understand how one gets the RHS. Could you please it? There must be some reasoning involved. Please help me. Thanks.

 

[micromass]

Isn't that an axiom?

 

[makehc]

Yes, it's distributivity.

x OR (y AND z) = (x OR y) AND (x OR z).

If the RHS is true, x must be true, or both y and z must be true, which is the statement of the LHS.

 

[chiro]

x+(y.z) = (x+y).(x+z)

I don't understand how one gets the RHS. Could you please it? There must be some reasoning involved. Please help me. Thanks.

One way to prove it is by using proof by exhaustion. If we were doing normal algebra we couldn't do this but because the state space of Boolean algebra is small in this example (8 possibilities) its easy to prove it in this way.

 

[jackson6612]

Isn't that an axiom?

Hi Micro

Isn't a postulate a same thing as an axiom? Perhaps, in mathematical terms there is a distinction but M-W does take them equivalent in some respects. Please let me know.

Thank you, everyone, for all the help. Makehc, your post was quite helpful.

 

[cobalt124]

Starting from RHS:

(x+y).(x+z)=x.x + x.z + x.y + y.z
=x + x.z + x.y + y.z
=x.(1 + z + y) + y.z
=x + (y.z)

Apologies if this is teaching granny to suck eggs, or indeed if it's wrong. This is how I would visualise it.

 

[micromass]

Hi Micro

Isn't a postulate a same thing as an axiom? Perhaps, in mathematical terms there is a distinction but M-W does take them equivalent in some respects. Please let me know.

Thank you, everyone, for all the help. Makehc, your post was quite helpful.

Yes, a postulate is the exact same thing as an axiom (although there was a distinction in the past). But I always use the word axiom. Sorry for the confusion!

 

[jackson6612]

Yes, a postulate is the exact same thing as an axiom (although there was a distinction in the past). But I always use the word axiom. Sorry for the confusion!

No worries!

 

[jackson6612]

Starting from RHS:

(x+y).(x+z)=x.x + x.z + x.y + y.z
=x + x.z + x.y + y.z
=x.(1 + z + y) + y.z
=x + (y.z)

Apologies if this is teaching granny to suck eggs, or indeed if it's wrong. This is how I would visualise it.

Cobalt: Thank you. BTW, I'm no granny, just a layman!

 

[jackson6612]

x+(y.z) = (x+y).(x+z)

Isn't there any other expression(s) which could be equivalent in value to the quoted expressions? Something like (x+y).(x+z).(z.z)? I know it's wrong; I'm simply trying to explain what I have asked you for. Thanks.

 

[cobalt124]

Ha Ha, and I managed to insult you as well! It's teaching YOUR granny to suck eggs. I should find out where the expression came from before I use it.