Initial work

CS1029/practical-2023-10-13/sets

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+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