1. a) the students who either live within 1 mile of the school or who walk to classes
   b) the students who live within 1 mile of the school and walk to classes
   c) the students who live within 1 mile of the school and do not walk to classes
   d) the students who walk to classes and do not live within 1 mile of the school

2. a) { 0, 1, 2, 3, 4, 5, 6 }
   b) { 3 }
   c) { 1, 2, 4, 5 }
   d) { 0, 6 }

3. a) { a, b, c, d, e, f, g, h }
   b) { a, b, c, d, e }
   c) {}
   d) { f, g, h }

5. A \union B = { x | x in A || x in B }; commutative as OR is commutative
   A \intersect B = { a | x in A && x in B }; commutative as AND is commutative

6. A - B = { x | x \in A \and x \nin B }
   !B = { x | x \nin B }
   A & !B = { x | x \in A \and x \in !B } = { x | x \in A \and x \nin B }

   (A & B) | (A & !B) = (A | A) & (B | !B) (distribution of & over |)
   = A & U
   = A

7. a) { 4 6 }
   b) { 0 1 2 3 4 5 6 7 8 9 10 }
   c) { 4 5 6 8 10 }
   d) { 0 2 4 5 6 7 8 9 10 }

9. { 2 5 }

11. A ^ B = { x | x in A ^ x in B } = { x | (x in A | x in B) & !(x in A & x in B) }
          = { x | x in A | x in B } - { x | x in A & x in B }
		  = (A | B) - (A & B)

12. a) { a: 3, b: 3, c: 1, d: 4 }
    b) { a: 2, b: 2 }
	c) { a: 1, c: 1 }
	d) { b: 1, d: 4 }
	e) { a: 5, b: 5, c: 1, d: 4}

14. A_i = { x | x in Z, x <= i }
    a) A_1
	b) A_n