Fiber of Truth/Examples
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Examples of Solution Sets
Solution Set of $x^2 = 2$ in $\R$
Let $x$ denote a variable whose domain is the set of real numbers $\R$.
Let $\map P x$ be the propositional function defined as:
- $\map P x := x^2 - 2$
Then the solution set of $\map P x$ is $\set {\sqrt 2, -\sqrt 2}$.
Solution Set of $x^2 = 2$ in $\Q$
Let $x$ denote a variable whose domain is the set of real numbers $\Q$.
Let $\map P x$ be the propositional function defined as:
- $\map P x := x^2 - 2$
Then the solution set of $\map P x$ is the empty set $\O$.
Solution to $x^2 - 2 x - 3$
Consider the equation in algebra:
- $x^2 - 2 x - 3 = 0$
where the domain of $x$ is implicitly taken to be the set of real numbers $\R$.
Then $3$ is a solution to $x^2 - 2 x - 3 = 0$.