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every natural belonging to A or B, at least one of: k +17 \in A , k-31 \in B

Source: Tuymaada Junior 2004 p4

May 11, 2019
SetsSubsetspartitionpartitionsalgebra

Problem Statement

Given the disjoint finite sets of natural numbers A A and B B , consisting of n n and m m elements, respectively. It is known that every natural number belonging to A A or B B satisfies at least one of the conditions k+17∈A k + 17 \in A , k−31∈B k-31 \in B . Prove that 17n=31m 17n = 31m
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