Given: $$A = \{x: 1 \le x \le 5\}$$ why is $$A' = \{x : x 5\}$$ and not $$A' = \{x: x 5\}$$

Question

Given: $$A = \{x: 1 \le x \le 5\}$$ why is $$A' = \{x : x < 1 \vee x > 5\}$$ and not $$A' = \{x: x< 1 \wedge x > 5\}$$

anonymous · Answer

Since $x$ cannot be both less than one and greater than five at one time (otherwise we have a logical contradiction). Also, De Morgan's laws are useful for this.

lgbasallote · Answer

so does that mean $$A = \{x : x \ge 1 \wedge x \le 5\}$$

anonymous · Answer

In any case:
$$
A=\{x|1\leq x\leq 5\}=\{x|1\leq x \wedge x\leq 5\}
$$

anonymous · Answer

Yessir.

lgbasallote · Answer

i can't believe i didn't think of that first reason....

anonymous · Answer

Unless your x's can quantum tunnel . . .

lgbasallote · Answer

uh-oh....math conversation.....time to leave..

anonymous · Answer

(Sorry, I've been hanging out in the Physics section too long)

anonymous · Answer

Go go, quantum entanglement and random transmission of data!

anonymous · Answer

Strange things can happen in this here multiverse.