When we replace both variables by individuals we obtain a statement. For example, Peter is older than Susan is a statement obtained by replacing both x and y by members of the sets of men and women in the group. Paris, Bangkok, NewDelhi. We may put a universal quantifier with one variable, or an existential quantifier with one variable, in front of an incomplete statement with two variables. This gives a new incomplete statement with only the other variable.
Every man is taller than y , where y is a woman in the group.
At least one man is taller than y , where y is a woman in the group. Let x stand for a train, and let y stand for a railway station. We may put two universal quantifiers in front of an incomplete statement containing two variables. These two statements have the same meaning. For example, let x stand for a man and let y stand for a woman in a group of people.