## anonymous 3 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. anonymous

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. anonymous

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

3. anonymous

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

4. anonymous

Yessir.

5. anonymous

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

6. anonymous

Unless your x's can quantum tunnel . . .

7. anonymous

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

8. anonymous

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

9. anonymous

Go go, quantum entanglement and random transmission of data!

10. anonymous

Strange things can happen in this here multiverse.

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