## tux Group Title Prove: A\(B∪C)=(A\B)∩(A\C) one year ago one year ago

1. abayomi12 Group Title

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

2. abayomi12 Group Title

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.

3. satellite73 Group Title

why these answers get more and more random as the day goes on

4. helder_edwin Group Title

\[ \large A\setminus(B\cup C)=A\cap(B\cup C)^c =A\cap(B^c\cap C^c) \] \[ \large A\cap A\cap B^c\cap C^c=(A\cap B^c)\cap(A\cap C^c)= \]