Question

2. For a subset X = {21,402...
{1,2,...) of the set of positive integur, XX denotes the set
{x} +3; : *j} and X denotes the number of elements in X
(a) Find subsets A, B of positive integers such the BB und
A+A= B + B.
(b) Do there exist subsets A, B of positive integers such that B = 3,4 B
and A+A= B B2
(e) Show that if n = 2, then there ist sulla positive inters such that
A] = B] = , A Band 1 + A + B​

Answer 1

Answer:

Where 0 means that the element i∉A∪B , 1 means i∈A and 2 means i∈B. Clearly with A∩B=∅ . If we consider A and B distinguishable (A=1  B=2 is different from A=2  B=1), then the answer is simply:

3n

The number of ternary numbers of n ciphers. Viceversa if the set are not distinguishable, we must divide this number for 2!=2 , subtracting clearly the only case that doesn't have permutations(A=B=∅):

3n−12

Then we must add the empty sets case we subtracted before and we'll have:

3n+12

Step-by-step explanation: