Exercise 5

Write the negation, converse and contrapositive for each of the statements below.

1. If the power goes off, then the food will spoil.

2. If the door is closed, then the light is off.

3. $\forall x (x \lt 1 \to x^2 \lt 1)$.

4. For all natural numbers $n$, if $n$ is prime, then $n$ is solitary.

5. For all functions $f$, if $f$ is differentiable, then $f$ is continuous.

6. For all integers $a$ and $b$, if $a\cdot b$ is even, then $a$ and $b$ are even.

7. For every integer $x$ and every integer $y$ there is an integer $n$ such that if $x > 0$ then $nx > y$.

8. For all real numbers $x$ and $y$, if $xy = 0$ then $x = 0$ or $y = 0$.

9. For every student in Math 321, if they do not understand implications, then they will fail the exam.