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tux

Prove: A\(B∪C)=(A\B)∩(A\C)

  • one year ago
  • one year ago

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  1. abayomi12
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    Indirect proof means assume the opposite and find a contradiction. If a + c > b + c then a > b

    • one year ago
  2. abayomi12
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    assume that a < b Then there exists a positive number such that a+X = b Now, plug this value into the first part... a + c > (a+X) + c So (a + c) > (a + c) + X So, a number PLUS a positive number is less than the number itself? This is a contradiction. So it is not the case that a < b Part 2: assume a = b a + c > a + c No number (a+c) can be greater than itself, so this is a contradiction. So, it is not the case that a = b So, a is not <= b So a > b By the way, it doesn't matter if a, b or c = 0, the simply can't equal each other.

    • one year ago
  3. satellite73
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    why these answers get more and more random as the day goes on

    • one year ago
  4. helder_edwin
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    \[ \large A\setminus(B\cup C)=A\cap(B\cup C)^c =A\cap(B^c\cap C^c) \] \[ \large A\cap A\cap B^c\cap C^c=(A\cap B^c)\cap(A\cap C^c)= \]

    • one year ago
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