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## lgbasallote Group Title Given: $A = \{x: 1 \le x \le 5\}$ why is $A' = \{x : x < 1 \vee x > 5\}$ and not $A' = \{x: x< 1 \wedge x > 5\}$ one year ago one year ago

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1. LolWolf Group Title

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.

2. lgbasallote Group Title

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

3. LolWolf Group Title

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

4. LolWolf Group Title

Yessir.

5. lgbasallote Group Title

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

6. CliffSedge Group Title

Unless your x's can quantum tunnel . . .

7. lgbasallote Group Title

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

8. CliffSedge Group Title

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

9. LolWolf Group Title

Go go, quantum entanglement and random transmission of data!

10. CliffSedge Group Title

Strange things can happen in this here multiverse.