Page 12 - Discrete Structure II

3. ∅ ∈ P (A)

True, it is an element in P (A)

4. ∅ ⊂ A

True

5. ∅ ⊂ P (A)

False

6. {a} ∈ A

False

7. ∅ ∈ P (A)

True

8. {a} ⊂ A

True

9. {a} ⊂ P (A)

False

Relation on a set

A binary relation on a set A, is a relation from A to A.

Example

A = {a, b, c}
A x A = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}

The following are relations on the set A
1. {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}
2. { (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}
3. {(a, a)}