View source for Verity

A '''verity''' is a statement which is true for all alternatives in a limited set.

Suppose we have a [[cell]] '''A''' and as cell '''B'''. Consider the following [[implication]] [[chain]]s:
 A=1 => ... => B=2
 A<>1 => ... => B=2
Cell '''A''' can either contain [[digit]] 1 or it does not. There is no middle ground. When both situations lead to the placement of digit 2 in cell '''B''', this cell must contain digit 2. This is a verity.

The alternative term '''veracity''' is sometimes used for similar purposes, but there is no real distinction between these two terms.

The following situation shows how a verity can also be proven when there are more than 2 alternatives:
 A=(1,2,3)
 A=1 => ... => B=2
 A=2 => ... => B=2
 A=3 => ... => B=2
In this sample, cell '''A''' has candidates for digits 1,2 and 3. Each of these force digit 2 in cell '''B'''.
== See Also ==
* [[Forcing Chain]]
* [[Tabling]]