Determine boolean conjunctive query are cyclic or acyclic, Mathematics

Determine boolean conjunctive query are cyclic or acyclic, Mathematics

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Are the following Boolean conjunctive queries cyclic or acyclic?

(a) a(A,B) Λ b(C,B) Λ c(D,B) Λ d(B,E) Λ e(E,F) Λ f(E,G) Λ g(E,H).

(b) a(A,B,C) Λ b(A,B,D) Λ c(C,D) Λ d(A,B,C,D).

(c) a(A,B,C) Λ b(A,B,D) Λ c(C,D) Λ d(C,E,F) Λ e(D,E,F).

If they are acyclic, give a join tree, if they are cyclic; give a hypertree decomposition of minimal width of the query.

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