## lgbasallote 2 years ago Given: $A = \{x: 1 \le x \le 5\}$ why is $A' = \{x : x < 1 \vee x > 5\}$ and not $A' = \{x: x< 1 \wedge x > 5\}$

1. LolWolf

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

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

3. LolWolf

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

4. LolWolf

Yessir.

5. lgbasallote

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

6. CliffSedge

Unless your x's can quantum tunnel . . .

7. lgbasallote

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

8. CliffSedge

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

9. LolWolf

Go go, quantum entanglement and random transmission of data!

10. CliffSedge

Strange things can happen in this here multiverse.