If 𝑅(𝑥, 𝑦) = “𝑥 𝑟𝑒𝑙𝑖𝑒𝑠 𝑢𝑝𝑜𝑛 𝑦, ” express the following in unambiguousEnglish:a. ∀𝑥 ∃𝑦 𝑅(𝑥, 𝑦)b. ∀𝑦 ∃𝑥 𝑅(𝑥, 𝑦)c. ∀𝑥 ∀𝑦 𝑅(𝑥, 𝑦)

To express the predicates in unambiguous English, we need to clarify the meaning of the symbols and their arrangement in the context of the statement $R(x, y) =$ "x relies upon y."

1. Expressing ∀x ∃y R(x, y):

   • This expression states that "For every x, there exists a y such that x relies upon y."
   • In plain English, it means: "Every individual x relies upon at least one individual y."

2. Expressing ∀y ∃x R(x, y):

   • This expression indicates that "For every y, there exists an x such that x relies upon y."
   • In clearer terms: "Every individual y is relied upon by at least one individual x."

3. Expressing ∀x ∀y R(x, y):

   • This expression signifies that "For every x and for every y, x relies upon y."
   • Thus, in unambiguous English: "Every individual x relies upon every individual y."

Summary

In summary, the translations of the logical expressions into unambiguous English are as follows: a. "Every individual x relies upon at least one individual y." b. "Every individual y is relied upon by at least one individual x." c. "Every individual x relies upon every individual y."