You must use a **counter example** to prove that a statement is **false**.

For example, "All numbers are even numbers."

The counter example can be that 5 is odd, not even.

Let `p(n)`

be `"n divides 77"`

.

Write propositions below in words and tell whether it is true or false.

Assume that `n`

is a **positive integer**.

`p(11)`

Let `p(x)`

be `"x ≥ x`

.^{2}"

Tell whether each proposition below is true or false.

Assume that `x`

is a real number which includes a decimal number.

Let `P(x)`

denote `"x is a professional athlete."`

Let `Q(x)`

denote `"x plays soccer."`

The domain of discourse is the set of all people.

Write each proposition below in words.

Determine the truth value of each statement.

- Write negation for
- Write negation for