Question

This is like multiple choice but you have to choose all of the correct answers. If the domain of x is: a, b, c, which of the following is logically equivalent to VxP(x)? O a. (P(a) A P(b) A P(c)) b. P(a) A-P(b) A P(c) O c. 3x P(x) O d. -P(a) V-P(b) v PC) e. (P(a) v P(b) v P(c)) Of. 3xP(x) Og. None of the choices are correct h. 3xP(x) i. VxP(x) Oj. VxP(x)

Answer 1

For the given domain, the only logical equivalent to ∀xP(x) is (P(a) ∧ P(b) ∧ P(c)), where P is true for each domain element a, b, and c.

Step-by-step explanation:

The question seems to be asking to identify the logical equivalents given a domain of x which includes a, b, and c. In propositional logic, the statement ∀xP(x), which reads as "for all x, P(x) holds", is true if P(x) is true for every element in the domain of x. Thus, among the choices given, option a. (P(a) ∧ P(b) ∧ P(c)) is logically equivalent to ∀xP(x) because it asserts that P(x) holds for all instances of x in the given domain. The rest of the choices represent different logical constructs that do not match the universal quantifier ∀ applied to P(x).