1. Given that there are 100 elements in A1, 1000 in A2, and 10,000 in A3, ?nd the number of elements in A1 ∪A2 ∪A3 in each of the cases below. (a) A1 ⊆ A2 and A2 ⊆ A3 (b) the sets are pairwise disjoint
Draw, and use, relevant Venn diagrams in each case.
2. Consider the non negative integer solutions for the equation x1 + x2 + x3 + x4 + x5 = 40. (a) How many distinct solutions are there? (b) How many distinct solutions are there if x1 ≥ 10? (c) How many distinct solutions are there if x1 < 20? (d) How many distinct solutions are there if x1 < 20 and x2 < 5?
3. (a) Make a table of values for the function f(x,y,z) = xy + yz + (x + y)z and use it to convert the function to disjunctive normal form (a sum of products). (b) Use the laws for boolean algebras to convert g(x,y,z) = x(y + z) + (xy) (x + z) into disjunctive normal form.