Page 39 - Discrete Structure II
P. 39
0 0
1 0
1 1
Reflexivity - Symmetric
Consider the following zero-one matrix on a set A = { a, b, c} and the relation R represented by the
following matrix.
1 0 1
0 1 0
1 0 1
a. Is the relation reflexive? symmetric?
Answer:
It is reflexive because all diagonal entries are 1. R ={(a, a), (a, c), (b, b), (c, a), (c, c)}
It is also symmetric because the elements symmetric with respect to the diagonal are equal.
Exercise 2:
Consider the following matrix, is it reflexive? Symmetric?
1 0 1 1
1 1 0 1
1 0 0 1
1 1 0 1
Answer:
It is not reflexive, because there is one entry in the diagonal that is zero.
It is not symmetric because not all elements symmetric with respect to the diagonal are equal.
