Talk:Boolean algebra

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Monotone laws

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

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

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)

Why does Figure 3 miss out the exclusive or? http://www.ivorcatt.org/exclusive-or.htm Ivor Catt — Preceding unsigned comment added by 31.48.249.63 (talk) 13:33, 6 June 2017 (UTC)

Venn Diagrams

For x V y, shouldn't the intersecting circles be white, since x V y = x + y - (x ^ y)? (as in, OR does not include the product of x AND y). SquashEngineer (talk) 14:35, 2 November 2015 (UTC)

The venn diagrams are correct. XOR would have the overlapping area white. FreeFlow99 (talk) 09:31, 15 January 2016 (UTC)

Order of Operation

There are 7 normally used boolean operators (most used are And, Or, Exclusive-Or, Not; lesser used are If and only If / XNOR, NAND, NOR) plus one I've never actually seen being used (but is mentioned in this article): Material Implication, which gives 8 in total. The lists of Order of Operations I've managed to find on the internet only contain 3 of the operators: And, Or, and Not. Even if I assume that NAND has the same precedence as AND, and NOR the same as OR, that still only covers 5 of the 8. It would be useful if a table showing the Order of Operations, for all 8 operators, for boolean algebra were included in this article. Is there an expert who can add it? FreeFlow99 (talk) 09:42, 15 January 2016 (UTC)

"Boolean calculus"

What is the definition of "boolean calculus" that is used in this section of the article? Jarble (talk) 16:18, 10 July 2017 (UTC)

It originally was "boolean algebra," but someone replaced it last year with "boolean calculous [sic]". I suspect that this was vandalism, though I'm not sure. Jarble (talk) 16:44, 14 July 2017 (UTC)