Explain the types of quantifier.

Universal Quantifier:

Universal Quantifier is used for Universal Quantification and is denoted by ∀(for all). The Universal Quantification of P(x) is denoted by ∀xP(x) and ∀xP(x) is a proposition “p(x) is true for all the values of x in the universal set”. If x1,x2, x3,…, xn are the values in the universal set then the Universal Quantification ∀xP(x) is same as the conjunction P(x1) ˄ P(x2) ˄ P(x3) ˄ … ˄ P(xn).

Existential Quantifier:

Existential Quantifier is used for Existential Quantification and is denoted by ∃(there exist). The Existential Quantification of P(x) is denoted by ∃xP(x) and ∃xP(x) is a proposition “p(x) is true for at least one values of x in the universal set”. If x1,x2, x3,…, xn are the values in the universal set then the Existential Quantification ∃xP(x) is same as the disjunction P(x1) ∨ P(x2) ∨ P(x3) ∨ … ∨ P(xn).