What does a one-way if statement let us conclude?

A one-way if statement connects a condition to a required result. In the rule “If a piece is a square, it has a dot,” being a square is enough to require a dot. This is called a sufficient condition: once that condition holds, the stated result must hold too.

The complete pictured set contains a dotted square, a dotted circle and a triangle without a dot. The square meets the requirement because it has a dot. The rule does not require anything about whether circles or triangles have dots, so both of the other pieces are allowed.

Reversing the sentence gives a different rule: “If a piece has a dot, it is a square.” This reversal is called the converse. The dotted circle shows why the original rule does not establish its converse. A dot can occur without a square even though every square in this set has a dot.

A square without a dot would violate the original rule because its condition would hold while its required result did not. The reasoning depends on the exact one-way rule supplied here. It does not silently add “only squares have dots,” and it is not a claim that every everyday use of if has this same simple meaning.