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We say that $\\Phi$ is combinatorially similar to $\\Psi$ if there are bijections $f \\colon \\Phi(X^2) \\to \\Psi(Y^{2})$ and $g \\colon Y \\to X$ such that $\\Psi(x, y) = f(\\Phi(g(x), g(y)))$ for all $x$, $y \\in Y$. It is shown that the semigroups of binary relations generated by sets $\\{\\Phi^{-1}(a) \\colon a \\in \\Phi(X^{2})\\}$ and $\\{\\Psi^{-1}(b) \\colon b \\in \\Psi(Y^{2})\\}$ are isomorphic for combinatorially similar $\\Phi$ and $\\Psi$. 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