4. For the following statement, first write the formal statement and then its negation [10 points]

For all integers n, if n is prime then n is odd

Formal statement:

Negation:

5. For the following statement (1) write the statement informally without using variables or the symbols

V(for all) or 3(there exists), and (2) indicate whether the statement is true or false and briefly justify your answer.

v(for all) integers a, 3(there exists) an integer b such that a + b = 0.

6. Is the following argument valid or invalid? Justify your answer.

All real numbers have nonnegative squares,

The number i has a negative square

Therefore, the number i is not a real number.

7. Define the predicate F(x; y): x is a factor of y. Find the truth set of F(x, y) when the domain of x and y is

{13, 6, 8, 16}. Note that your truth set should consist of ordered pairs (x, y) that satisfy the given predicate.

8. Use a diagram to show that the following argument can have true premises and a false conclusion.

All dogs are carnivorous.

Aaron is not a dog.

Aaron is not carnivorous.