UCCM1363: Chapter 2

What is a predicate?

• A statement that is always true.

• A sentence that contains variables and becomes a statement when values are substituted.

• A type of mathematical function.

• A statement that cannot be evaluated.

What does the universal quantifier '∀' signify?

• At least one value is false.

• For all values.

• There exists at least one.

• None of the above.

What is the truth value of the statement '∀x ∈ ℤ, x + 1 < 4'?

• True for some integers only.

• True

• False

• Undefined

What is a counterexample?

• A value that makes a statement true.

• A value that makes a universal statement false.

• An example that illustrates a concept.

• A type of mathematical proof.

What does the existential quantifier '∃' mean?

• Any values.

• There exists at least one.

• For some values.

• For all values.

Which of the following is a correct negation of the statement '∀ primes p, p is odd'?

• ∀ primes p, p is even.

• ∀ primes p, p is not odd.

• ∃ a prime p such that p is not odd.

• ∃ a prime p such that p is odd.

What is the truth value of '∃x ∈ ℝ such that x^2 + 1 = 0'?

• True

• False

• Undefined

• True for some real numbers.

What is the formal version of the statement 'Some integers equal their own squares'?

• ∃ integers x such that x^2 = x.

• ∀ integers x, x^2 = x.

• ∃ integers x such that x^2 ≠ x.

• ∀ integers x, x^2 ≠ x.

What is the negation of the statement '∃x such that P(x)'?

• ∀x, P(x) is true for at least one x.

• ∀x, P(x) is false.

• ∀x, ~P(x).

• ∃x such that ~P(x).

What is the truth value of '∀x ∈ ℝ, x^2 ≥ 0'?

• True

• False

• True for some real numbers.

• Undefined