Asked by Angely Taveras on May 09, 2024
Verified
`Which of the following is the quantifier-negation rule?
A) (x) (…x…) (x) (\ldots x \ldots) (x) (…x…) . Therefore, (… (\ldots (… a ... ) ) )
B) ∼(x) (…x…) \sim(x) (\ldots x \ldots) ∼(x) (…x…) . Therefore, (∃x) ∼(…x…) (\exists x) \sim(\ldots x \ldots) (∃x) ∼(…x…)
C) (… (\ldots (… a .... ) ) ) . Therefore, (∃x) (…x…) (\exists x) (\ldots x \ldots) (∃x) (…x…)
D) (∃x) (…x…) (\exists x) (\ldots x \ldots) (∃x) (…x…) Therefore, (…a…) (\ldots \mathrm{a} \ldots) (…a…)
E) (… (\ldots (… a ... ) Therefore, (x) (…x…) (x) (\ldots x \ldots) (x) (…x…)
Negation
The contradiction or denial of something, or the operation of inverting the truth value in logic.
Quantifier-Negation Rule
A principle in formal logic that deals with the relationship between quantifiers and the negation of statements.
Quantifier
A symbol or word in logic that specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
- Identify and apply the quantifier negation rule correctly.
Verified Answer
LP
Lauren PurdyMay 14, 2024
Final Answer :
B
Explanation :
The quantifier-negation rule is that to negate a universal quantifier, we must use existential quantifier and negate the predicate. So, option B is the correct choice as it expresses the negation of a universal quantifier by an existential quantifier with negated predicate.
Learning Objectives
- Identify and apply the quantifier negation rule correctly.