Determine whether each sentence in is a proposition. If the...

Determine whether each sentence in is a proposition. If the sentence is a proposition, write its negation. (You are not being asked for the truth values of the sentences that are propositions.)
Every even integer greater than 4 is the sum of two primes.

Key Concepts

Universal Quantifier

The universal quantifier is a logical symbol used in expressions to denote that a particular property or statement applies to all members of a given set or domain. It is typically expressed using phrases like 'every' or 'for all', and its proper negation results in an existential claim.

Existential Quantifier

The existential quantifier is used in logic to represent that there exists at least one element in a domain for which a given property holds. When negating a universally quantified proposition, it becomes necessary to express the existence of a counterexample using the existential quantifier.

Proposition

A proposition is a declarative sentence that claims something and possesses a clear truth value—either true or false. In logic, it forms the building block for constructing logical arguments and analyses.

Negation

Negation is the logical operation that reverses the truth value of a proposition. The negated statement is true when the original is false, and vice versa. Constructing the negation of a proposition is fundamental in logic, especially when dealing with proofs and counterexamples.

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