21.1.2. Tutorial 3

Try these first

1. 1.

   Is {2} a subset of {1, 2, 3}?

   Hint

   Check if all elements of the first set are in the second set.

2. 2.

   What is the definition of a symmetric relation?

   Hint

   Consider the pairs involved in a symmetric relation.

3. 3.

   If (A ∩ C) ⊆ (B ∩ C), can we conclude A ⊆ B?

   • True
   • False

   Hint

   Think about how intersections dictate membership.

4. 4.

   Does an anti-symmetric relation allow both (a, b) and (b, a) if a ≠ b?

   • True
   • False

   Hint

   Recall the definition carefully.

5. 5.

   Demonstrate with a concrete example how a relation can be both symmetric and irreflexive.

   Hint

   Ensure no self-pairs are included for irreflexivity.

6. 6.

   Create a scenario where a non-empty set contains both reflexive and irreflexive relations, detailing how this is possible.

   Hint

   Reflect on the definitions carefully for overlaps.