Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: May 2016

Universal quantifiers:

The universal quantifier is a symbol of symbolic logic which expresses that the statements within its scope are true for everything, or every instance of a specific thing.

The symbol ∀, which appears as a vertically inverted “A”, is used as the universal quantifier. Universal quantifiers are normally used in logic in conjunction with predicate symbols, which say something about a variable or constant, in this case the variable being quantified.

Existential quantifiers:

The existential quantifier is a symbol of symbolic logic which expresses that the statements within its scope are true for at least one instance of something. The symbol ∃, which appears as a backwards “E”, is used as the existential quantifier. Existential quantifiers are normally used in logic in conjunction with predicate symbols, which say something about a variable or constant, in this case the variable being quantified.

Proof of Distribution law:

Consider Truth table for above expression:

Since from the above table last two columns are equal i.e. p v (q ^ r) ≡(p v q)^(p v r). Hence, distributive law is proved.