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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 \[A' = \{x: x< 1 \wedge x > 5\}\]

  • 2 years ago
  • 2 years ago

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  1. LolWolf Group Title
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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 years ago
  2. lgbasallote Group Title
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    so does that mean \[A = \{x : x \ge 1 \wedge x \le 5\}\]

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

    • 2 years ago
  4. LolWolf Group Title
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    Yessir.

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

    • 2 years ago
  6. CliffSedge Group Title
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    Unless your x's can quantum tunnel . . .

    • 2 years ago
  7. lgbasallote Group Title
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    uh-oh....math conversation.....time to leave..

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

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

    • 2 years ago
  10. CliffSedge Group Title
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    Strange things can happen in this here multiverse.

    • 2 years ago
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