Asked by Tiffany Dollente on May 03, 2024
Verified
The statement ~[(x) Px (x) Qx] is which kind of statement?
A) atomic singular statement
B) truth-functional compound of singular atomic statements
C) quantifier applied to atomic open sentence
D) truth-functional compound of open sentences within the scope of a quantifier
E) truth-functional compound of quantified statements
Truth-functional Compound
A compound statement whose truth value depends solely on the truth values of its components.
Quantifier
A logical tool that counts the instances within a discourse domain adhering to the conditions of an open formula.
Atomic Open Sentence
A type of statement in logic, which contains at least one variable, and becomes a proposition once the variables are replaced by specific values.
- Distinguish between individual atomic statements and multiple composite statements that incorporate quantifiers and operations based on truth values.
Verified Answer
ZC
Zehao ChengMay 05, 2024
Final Answer :
E
Explanation :
The statement involves quantifiers (indicated by the symbol "uf024" which stands for "there exists") applied to atomic open sentences (Px, Qx), and it is combined using a truth-functional operator (indicated by "uf0da" which stands for "or"). This makes it a truth-functional compound of quantified statements.
Learning Objectives
- Distinguish between individual atomic statements and multiple composite statements that incorporate quantifiers and operations based on truth values.