There are some boys and girls that study in a school. A group of boys is called sociable, if each girl knows at least one of the boys in the group. A group of girls is called sociable, if each boy knows at least one of the girls in the group. If the number of sociable groups of boys is odd, prove that the number of sociable groups of girls is also odd.
Problem
Source: X International Festival of Young Mathematicians Sozopol 2019, Theme for 10-12 grade
Tags: combinatorics, Sets