Question

For each of the following relations, say which of the properties of reflexivity, symmetry, and transitivity are satisfied and which fail.

13) S on the set, T, of all triangles in the plane defined by t₁St₂ iff t₁ and t₂ are similar.

14) R with domain ? and codomain the set, P, of all real polynomials in one unknown m defined by aRp iff a is a root of p.

15) R on the set P X L, where P is the set of all points in the plane, L is the set of all straight lines in the plane, and pRl means that the point p lies on the line l.

16) P on the set, A, of all people, where xPy means x is a parent of y.

Answer 1