Counting and boolean algebra

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Counting and Boolean Algebra 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 t

Reference no: EM13937723

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