Q3 Predicate, Quantifiers and Rules of Inference

There exist only two types of quantifiers, Universal Quantification and Existential Quantification.

• True

• False

Let P (x) denote the statement “x >7.” Which of these have truth value true?

• P (0)

• P (4)

• P (6)

• P (9)

Let Q(x) be the statement “x < 5.” What is the truth value of the quantification ∀xQ(x), having domains as real numbers.

• True

• False

Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers

• True

• False

Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?

• True

• False

Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?

• True

• False

The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

• ∃x(C(x) ∧ F (x))

• ∀x(C(x) ∧ F (x))

• ∃x(C(x) → F (x)

• ∀x(C(x) → F (x))

The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.

• ∀x (F (x) → P (x))

• ∀x (F (x) ∧ P (x))

• ∃x (F (x) ∧ P (x))

• ∃x (F (x) → P (x))

Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”

• Modus tollens

• Modus ponens

• Disjunctive syllogism

• Simplification

Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”

• Modus tollens

• Conjunction

• Hypothetical syllogism

• Simplification