If all proposition are dependent, is the truth value of the AND gate dependent as well?

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I have been thinking about a question. Let us take an AND gate. In this AND gate, every proposition is dependent on another proposition. Given that there is no circular dependence, I can understand that if the number of propositions is finite, then the truth value of the AND gate is dependent on a proposition outside of the AND gate. Does this hold true for an AND gate with infinite propositions as well?