ToT 2021-fall JO5

There were 20 participants in a chess tournament. Each of them played with each other twice: once as white and once as black. Let us say that participant $X{}$ is no weaker than participant $Y{}$ if $X{}$ has won at least the same number of games playing white as $Y{}$ and also has won at least the same number of games playing black as $Y{}$ . Do there exist for sure two participants $A{}$ and $B{}$ such that $A{}$ is not weaker than $B{}$ ?

Boris Frenkin