Talk:Boolean algebra

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‎Enumeration of Boolean Functions on 2 Variables[edit]

I see it in Boolean algebras canonically defined#Truth tables, but there may be a better location. It certainly doesn't belong in this article. — Arthur Rubin (talk) 18:41, 28 March 2013 (UTC)

Truth function #Table of binary truth functions. Incnis Mrsi (talk) 19:26, 28 March 2013 (UTC)
He's added still more unsourced material which doesn't belong in this article. I've removed it three times, he hasn't come here to justify his additions, and I can make no sense of the justification on my talk page. — Arthur Rubin (talk) 21:52, 28 March 2013 (UTC)

Derived operations: XOR[edit]

The paragraph first dealing with derived operations introduces the operation sign ⊕ without any former explanation, and leaves to the reader the deducing needed to understand that it means XOR. I believe it should be fixed, although since I'm not a native English speaker and a poor writer I'd rather leave it to someone else. Thoughts? Jordissim (talk) 17:53, 5 June 2013 (UTC)

As far as I can see, the paragraph includes a detailed enough explanation and a link to the relevant article. I think that’s quite sufficient.—Emil J. 18:19, 5 June 2013 (UTC)
You're completely right, my fault. I misread the opening section. Jordissim (talk) 20:07, 5 June 2013 (UTC)

Monotone laws[edit]

The section on Monotone laws is contradictory given that the X ∨ Y operation was previously defined to be equivalent to X + Y - XY. The section references X ∨ Y being equivalent to X + Y, without the additional term, in its separation of the two sets of laws.

Also, the Law of Distributivity of ∨ over ∧ is simply incorrect, which can be shown by setting X to be true and Y and Z false. ( X ∨ ( Y ∧ Z )) is true, but (( X ∨ Y ) ∧ ( X ∨ Z )) is false. — Preceding unsigned comment added by 128.101.13.199 (talk) 21:43, 21 September 2013 (UTC)

I guess I'm not seeing where the article says X ∨ Y is equivalent to X + Y. It only says it satisfies many of the same laws, which is true. Also the "equivalence" to x+y-xy is prefixed with "If the truth values 0 and 1 are interpreted as integers" with no mention of applicability to any other values for x and y besides truth values; certainly 7+7-7*7 is not 7, in fact x+y-xy is idempotent if and only if x is 0 or 1. Perhaps this is worth clarifying in the article.
How do you get "(( X ∨ Y ) ∧ ( X ∨ Z )) is false" when both X ∨ Y and X ∨ Z are true? Vaughan Pratt (talk) 21:04, 20 October 2013 (UTC)

Duality contemplations[edit]

Section 5.2. Digital logic gates:

The contemplations on De Morgan equivalents and the Duality Principle and what it could mean for the number of Boolean operations represented by AND and OR gates are not helpful in this section. Especially the last paragraph is quite obscure and grammatically goofed up. I suggest to remove the last 2 or 3 paragraphs here. Towopedia (talk) 09:51, 29 April 2014 (UTC)

For many readers of Wikipedia the entire article is surely not helpful. The question of which of the sixteen binary Boolean operations are representable with one AND or OR gate and inverters should be helpful for those interested in the design and analysis of Boolean circuits. The last sentence merely lists the eight such that are not so representable; I'll rephrase it, which may or may not help. Couldn't find the grammatical error, a hint please. Vaughan Pratt (talk) 16:30, 8 May 2014 (UTC)
Rephrased as promised. Let me know whether it helps. Vaughan Pratt (talk) 16:02, 9 May 2014 (UTC)

Boolean Algebra[edit]

There seems to be an error in the "Values" paragraph confusing OR and XOR. The error continues in the "Operations" paragraph where OR is said to be: x V y = x + y - (x * y).

204.235.238.54 (talk) 19:28, 13 March 2015 (UTC)Raining Sky 13 March 2015

It seems that this is you who confuses OR and XOR: It is easily to check that x + y - (x * y) is 0 if and only if both x and y are 0. This is exactly the definition of the truth table of OR. D.Lazard (talk) 20:36, 13 March 2015 (UTC)