Question 168
Find all pairs $(X, Y)$ of sets with positive integer elements, which fulfill the following conditions:
(1) each of the sets $X$ and $Y$ has three elements;
(2) $3 \in X$ and $5 \in Y$;
(3) the set $X \cap Y$ has exactly one element;
(4) if $a$ and $b$ are distinct elements of $X$, then $(a+b) \in Y$.
(1) each of the sets $X$ and $Y$ has three elements;
(2) $3 \in X$ and $5 \in Y$;
(3) the set $X \cap Y$ has exactly one element;
(4) if $a$ and $b$ are distinct elements of $X$, then $(a+b) \in Y$.