- #1

- 1,462

- 44

## Homework Statement

Rewrite the following statements in symbolic form:

a) If ##a## and ##b## are real numbers with ##a \ne 0##, then ##ax+b=0## has a solution.

b) If ##a## and ##b## are real numbers with ##a \ne 0##, then ##ax+b=0## has a unique solution.

## Homework Equations

## The Attempt at a Solution

Attempts at solution:

Let ##P(x,a,b)## be the statement that ##ax+b=0## is true.

a) ##\forall a \in \mathbb{R} - \{0\} \forall b \in \mathbb{R} \exists x \in \mathbb{R} P(x,a,b)##

b) ##\forall a \in \mathbb{R} - \{0\} \forall b \in \mathbb{R} \exists x \in \mathbb{R} (P(x,a,b) \wedge \forall y (P(y,a,b) \implies y=x))##

Is that at all right? Is there an easier way? It all seems very cumbersome.