17.2.1. Definition and Characteristics

Try these first

1. 1.

   Define an irreflexive relation.

   Hint

   Think of self-relationships.

2. 2.

   What must be true for a relation to be considered symmetric?

   Hint

   Look for mutual connections.

3. 3.

   What is an irreflexive relation?

   Hint

   Look at the pairs in relation.

4. 4.

   If (a, b) belongs to a symmetric relation, then which of the following must also be true?

   • (b
   • a) is in the relation
   • (a
   • b) is not in the relation
   • None of the above

   Hint

   Refer back to the definition of symmetry.

5. 5.

   Consider the relation R defined on the set A = {1, 2, 3}: R = {(1, 2), (2, 3), (1, 3)}. Is R irreflexive and transitive?

   Hint

   Check for self-involvement for irreflexivity and chain linking for transitivity.

6. 6.

   Given the relation R = {(1, 2), (2, 3), (2, 1)}. Determine whether it is symmetric and explain.

   Hint

   Analyze individual connections for symmetry.