This type of function, such as f = x+y, produces the same output when the order of the inputs are altered.
A relation is said to possess the "anti" type of this property when it implies A and B are equal if the relation holds for A to B and B to A. This property also gives its name to a set theory operation which takes as inputs sets A and B, and returns the difference of elements that are found in either set, but not both sets. This type of function, such as f = x+y, produces the same output when the order of the inputs are altered. In linear algebra, this type of matrix is equal to its own transpose. In order for a relation to be an equivalence relation, it must possess transitivity, reflexivity and this other property. For 10 points, name this common mathematical property, which for a polygon, implies that an axis can be drawn through the polygon to create two mirror images.
A relation is said to possess the "anti" type of this property when it implies A and B are equal if the relation holds for A to B and B to A.
symmetric [accept word forms]