Given that there are 100 elements in a1 1000 in a2 and 10


1. Given that there are 100 elements in A1, 1000 in A2, and 10, 000 in A3, find 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.

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Science: Given that there are 100 elements in a1 1000 in a2 and 10
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