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Compute the Betti numbers of the abstract simplicial complex X with vertex set V(X) = {A, B, C, D, E, F}, and 1- and 2-simplices

Compute the Betti numbers of the abstract simplicial complex X with vertex set V(X) = {A, B, C, D, E, F}, and 1- and 2-simplices given by the respective sets {AB, AD, AE, BC, BD, BE,CD, DE} and {ABC}. Draw a picture of a geometric realization of this complex?

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