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Statement 1: My bedroom door is open.

Statement 2: My bedroom door is closed.

[Definition: closed is equivalent to not open. So statement 2 is the negation of statement 1.]

Now when I evaluate the truthfulness of statements 1 and 2...

We can translate this to a more formal logical setting by introducing the unary predicate O standing for openness and constant d, which means my bedroom door.

In this setting, statement 1 is Od and statement 2 is -Od [where - is a negation symbol]. I'm trying to figure out the truthfulness of the two statements Od and -Od.

This is where I get stuck because I suspect that BOTH Od and -Od are

*vacuously true*as the set of all possible states of the door, which would usually have two elements in it, open and not open, is

**empty**.

Since -Od is true, albeit vacuously, that means --Od is false. Since --Od is equivalent to Od, Od is false. And therefore, Od is

*true and false*.

**What is the flaw with my reasoning?**This smells to me like the "proof" that 1=2...