Predicate Logic - Formulating Arguments Flashcards
By the end of this deck, learners will be proficient in translating complex natural language statements into precise predicate logic expressions. They will develop the skills to critically evaluate the structure and validity of arguments formulated in predicate logic and understand the application of logical equivalences to simplify and analyze these arguments effectively.
How do you translate “All humans are mortal” into predicate logic?
∀x (Human(x) → Mortal(x))
How would you express “Some birds can fly” in predicate logic?
∃x (Bird(x) ∧ CanFly(x))
What predicate logic formula represents “There exists a cat that is not black”?
∃x (Cat(x) ∧ ¬Black(x))
Translate “Every student loves some teacher” into predicate logic.
∀x (Student(x) → ∃y (Teacher(y) ∧ Loves(x, y)))
Express in predicate logic: “No dogs are cats.”
∀x (Dog(x) → ¬Cat(x))
How do you represent “At least one student passed every exam” in predicate logic?
∃x (Student(x) ∧ ∀y (Exam(y) → Passed(x, y)))
What is a universal instantiation in predicate logic?
It’s a rule of inference that allows you to deduce specific instances from a universally quantified statement (from ∀x P(x) to P(c) for a specific c).
Define existential generalization in predicate logic.
It’s a rule of inference that allows you to infer an existentially quantified statement from a specific instance (from P(c) to ∃x P(x)).
What rule of inference lets you deduce Q from “P implies Q” and “P”?
Modus ponens.
How does the rule of universal generalization work in proofs?
If you’ve derived a property for an arbitrary object, you can generalize it to all objects in the domain.
What is modus tollens in the context of predicate logic?
It’s a rule of inference that allows you to infer ¬P from P → Q and ¬Q.
How would you demonstrate a statement is a tautology in predicate logic?
Show that the statement is true under all possible interpretations of its variables.
What predicate logic formula corresponds to “Every action has an equal and opposite reaction”?
∀x (Action(x) → ∃y (Reaction(y) ∧ EqualOpposite(x, y)))
How can contradiction be used in predicate logic proofs?
If assuming ¬P leads to a contradiction, you can conclude P (proof by contradiction).
What does it mean to bind a variable in predicate logic?
A variable is bound when it is quantified by a universal or existential quantifier within its scope.
