Reference no: EM13937716
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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: 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.
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