In 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer.
Let A be the set of all lines in the plane. A relation R is defines on A as follows. For every
To justify whether the given relation is reflexive, symmetric, transitive, or none of these.
Given information:
Let A be the set of all lines in the plane. A relation R is defined on A as follows:
For all l1 and l2 in A, l1R l2 ⇔ l1 is perpendicular to l2.
Calculation:
Reflexive:
The relation R is reflective if
Since a line is never perpendicular to itself,
Thus, R is not reflexive.
Symmetric:
The relation R on a set A is symmetric if
Let us assume that