Question

Suppose R(x,y) is the predicate “x understands y,” the universe of discourse for x is the set of students in Discrete Class, and the universe of discourse for y is the set of examples in these lecture notes. 

Translate the following into English:

∃x∀yR(x,y)

Answer 1

Let $R(x,y)$ be the predicate “$x$ understands $y$ ”, the universe of discourse for $x$ is the set of students in Discrete Class, and the universe of discourse for $y$ is the set of examples in these lecture notes.

Let us translate into English $∃x∀yR(x,y):$

There exists a student in Discrete Class that understands all examples in these lecture notes.