1. a) {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5), (5, 5) }
	Reflexive: \forall x. (x, x) \in R
	Antisymmetric (& not symmetric): all pairs have x <= y. forall x, y. x <= y, !(y <= x) || y == x
	Transitive
   b) {(1, 2), (1, 4), (2, 1), (2, 3), (3, 2), (3, 4), (4, 1), (4, 3)}
	Not reflexive: there are no pairs of (x, x)
	Symmetric - all pairs have their reverse represented
	Not antisymmetric: symmetric and anti-symmetric are mutually exclusive
	Not transitive: (1, 2) and (2, 3) - 1 + 3 is not odd

2. {(item, quantity)}
   {(Name, {(key, value)})}
   {(Name, Address, {(Room type, price, {(key, value)})}, ...)}

3. 105 305 306 505 705 707 905 906 909

4. a) ab ac bc cb
   b) {(a, a), (a, b), (a, c), (b, b), (b, a), (b, c), (c, a), (c, b), (d, d)}

5.a) {(1, 1), (1, 2), (1, 4), (2, 1), (2, 3), (3, 2), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4)}
	Not reflexive: (2, 2) is not present
	Symmetric, therefore not anti-symmetric
	Not transitive: (1, 2) and (2, 3), but not (1, 3)

  b) 12 21 14 41 32 23 43 34
	Not reflexive
	Symmetric, therefore not antisymmetric
	Not transitive: 12 and 23 but not 13

6. 1 1 0 0
   1 1 0 0
   1 0 1 1
   0 0 0 1

Yes, it's reflexive

8. {(a, b) | a divides b OR b divides a}
9. No, it's not transitive. (a, b) & (b, d), but not (a, d)
10. a) Not equivalence relation: missing transitivity
		(1, 3) and (3, 2), but not (1, 2)
	b) {0}, {1, 2}, {3}
11. \forall n \in N_0:
	0 + 3n
	1 + 3n
	2 + 3n

12. a) Y
    b) N: 0 is in both - not disjoint
	c) Y
	d) N: 0 is missing

13. a) 00 11 22 33 44 55 12 21 34 43 35 53 45 54 
    b) 00 11 22 33 44 55 01 10 23 32 45 54
	c) 00 11 22 33 44 55 01 10 02 20 12 21 34 43 35 53 45 54

14. a) Y, trivially
    b) N: not antisymmetric ((2, 3) and (3, 2))
	c) N: not reflexive (no (3, 3))