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Verity

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

Suppose we have a cell A and a cell B. Consider the following implication chains:

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.

Verity

See Also