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lgbasallote

  • 3 years ago

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

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  1. LolWolf
    • 3 years ago
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    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
    • 3 years ago
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    so does that mean \[A = \{x : x \ge 1 \wedge x \le 5\}\]

  3. LolWolf
    • 3 years ago
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    In any case: \[ A=\{x|1\leq x\leq 5\}=\{x|1\leq x \wedge x\leq 5\} \]

  4. LolWolf
    • 3 years ago
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    Yessir.

  5. lgbasallote
    • 3 years ago
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    i can't believe i didn't think of that first reason....

  6. CliffSedge
    • 3 years ago
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    Unless your x's can quantum tunnel . . .

  7. lgbasallote
    • 3 years ago
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    uh-oh....math conversation.....time to leave..

  8. CliffSedge
    • 3 years ago
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    (Sorry, I've been hanging out in the Physics section too long)

  9. LolWolf
    • 3 years ago
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    Go go, quantum entanglement and random transmission of data!

  10. CliffSedge
    • 3 years ago
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    Strange things can happen in this here multiverse.

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