21.4.2. Part B: Anti-Symmetric Relations

Try these first

1. 1.

   Define an anti-symmetric relation and provide one example.

   Hint

   Consider how elements relate to themselves.

2. 2.

   Are all diagonal pairs included in an anti-symmetric relation?

   Hint

   Think about the relationship a has with itself.

3. 3.

   What characterizes an anti-symmetric relation?

   • If (a
   • b) then (b
   • a) must be present
   • If (a
   • b) and (b
   • a)
   • then a = b
   • None of the above

   Hint

   Think about the consequence of pairs being included.

4. 4.

   Is the relation (3, 2) and (2, 3) anti-symmetric?

   • True
   • False

   Hint

   Examine how values compare.

5. 5.

   Given a set S of 5 distinct elements, find and justify the number of anti-symmetric relations possible.

   Hint

   Remember to take each element and its pairing into account.

6. 6.

   Construct an anti-symmetric relation on a set with 3 elements that includes at least 2 pairs.

   Hint

   Explore using pairings to design your valid relations.