It may be helpful for you. consider the proposition: "All of my friends are either wealthy or clever."
Using predicates, we can symbolise this as:
∀ x, friend(x) ⇒ (wealthy(x) ∨ clever(x))
However, if we agreed that the variable x can only stand for one of my friends, then we could symbolise this more simply as:
∀ x, wealthy(x) ∨ clever(x)
For a given propositional function P(x), the universe of discourse is the set from which the value of x may be chosen. Defining a universe of discourse can simplify the symbolisation of propositional functions. If a universe of discourse is not defined, then we shall have to assume that any object or individual may be substituted for x.