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Define $$A\\cdot B=\\{x\\cdot y:x\\in A, y\\in B\\}.$$ In this paper, we consider the following class of self-similar sets with overlaps. Let $K$ be the attractor of the IFS $\\{f_1(x)=\\lambda x, f_2(x)=\\lambda x+c-\\lambda,f_3(x)=\\lambda x+1-\\lambda\\}$, where $f_1(I)\\cap f_2(I)\\neq \\emptyset, (f_1(I)\\cup f_2(I))\\cap f_3(I)=\\emptyset,$ and $I=[0,1]$ is the convex hull of $K$. 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