What is quantification? Write a note on the quantification rules.

Quantification, in logic,it is  the attachment of signs of quantity to the predicate or subject of aproposition. The universal quantifier, symbolized by (∀-) or (-), where the blank is filled by a variable, is used to express that the formula following holds for all values of the particular variable quantified. Theexistential quantifier, symbolized (∃-), expresses that the formula following holds for some (at least one) value of that quantified variable.

Quantifiers of different types may be combined. For example, restricting epsilon (ε) and delta (δ) to positive values, b is called the limit of a function f(x) as x approaches a if for every ε there exists a δ such that whenever the distance from x to a is less than δ, then the distance from f(x) to b will be less than ε; or symbolically:

in which vertical lines mark the enclosed quantities as absolute values, < means “is less than,” and ⊃ means “if . . . then,” or “implies.”

Variables that are quantified are called bound (or dummy) variables, and those not quantified are called free variables. Thus, in the expression above, ε and δ are bound; and x, a, b, and ___ _______ ________ _________ ___ _____ ____ ________ ___.
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