1.5 Quantifiers & Predicate Logic

Propositions with Quantifiers


Determine which propositions are true when the variables range over:

  1. the nonnegative integers.

    Exercise 1

    Counterexample for 2: Let \(x = 1\).

    Counterexample for 4: Let \(x = 100\).

  2. the integers.

    Exercise 2

    Counterexample for 2: Let \(x = 1\).

  3. the real numbers.

    Exercise 3

    Counterexample for 3: Let \(x = 9.5\).