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example in this example so here this is the predicate formula and bound variable can be denoted by b free variable can be denoted by f scope of the quantifier can be denoted by yes so here first one for all x p of x comma y okay here x and y are called as subject or variables so p is called as a predicate this predicate belongs to only two subjects for our two variables that is x and y okay here for the variable x it is bounded with the universal quantifier that is for all x but y is not bounded with any uh quantifier either a universal quantifier or a existential quantifier here x is called as bounded variable y is called as free variable here the bounded variable is x free variable is y okay scope of the quantifier means here the quantifier is universal quantifier the predicate formula immediately followed by the universal quantifier okay after the universal quantifier what is the predicate formula is that p of x comma y now p of x comma y can be treated as the scope of the quantifi
