In this paper we consider compound conditionals, Fréchet-Hoeffding bounds and the probabilistic interpretation of Frank t-norms. By studying the solvability of suitable linear systems, we show under logical independence the sharpness of the Fréchet-Hoeffding bounds for the prevision of conjunctions and disjunctions of n conditional events. In addition, we illustrate some details in the case of three conditional events. We study the set of all coherent prevision assessments on a family containing n conditional events and their conjunction, by verifying that it is convex. We discuss the case where the prevision of conjunctions is assessed by Lukasiewicz t-norms and we give explicit solutions for the linear systems; then, we analyze a selected example. We obtain a probabilistic interpretation of Frank t-norms and t-conorms as prevision of conjunctions and disjunctions of conditional events, respectively. Then, we characterize the sets of coherent prevision assessments on a family containing n conditional events and their conjunction, or their disjunction, by using Frank t-norms, or Frank t-conorms. By assuming logical independence, we show that any Frank t-norm (resp., t-conorm) of two conditional events A|H and B|K, Tλ(A|H,B|K) (resp., Sλ(A|H,B|K)), is a conjunction (A|H)∧(B|K) (resp., a disjunction (A|H)∨(B|K)). Then, we analyze the case of logical dependence where A=B and we obtain the set of coherent assessments on A|H,A|K,(A|H)∧(A|K); moreover we represent it in terms of the class of Frank t-norms Tλ, with λ∈[0,1]. By considering a family F containing three conditional events, their conjunction, and all pairwise conjunctions, we give some results on Frank t-norms and coherence of the prevision assessments on F. By assuming logical independence, we show that it is coherent to assess the previsions of all the conjunctions by means of Minimum and Product t-norms. In this case all the conjunctions coincide with the t-norms of the corresponding conditional events. We verify by a counterexample that, when the previsions of conjunctions are assessed by the Lukasiewicz t-norm, coherence is not assured. Then, the Lukasiewicz t-norm of conditional events may not be interpreted as their conjunction. Finally, we give two sufficient conditions for coherence and incoherence when using the Lukasiewicz t-norm.