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anonymous

  • 4 years ago

For all numbers a and b, let a(.)b be defined by a (.) b = ab + a + b. For all numbers x, y, and z, which of the following must be true? #1. x(.)y = y (.) x #2. (x-1) (.) (x+1) = (x(.)x)-1 #3. x(.) (y+z) = (x (.) y ) + (x (.) z) ***the places that i have the "(.)" symbol, its because there is a dot with a circle around it in my book, ive never seen it before!

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  1. anonymous
    • 4 years ago
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    ah you are checking to see if it is commutative. so lets do it

  2. anonymous
    • 4 years ago
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    I've never studies that, that i recall, but its gonna be on my SAT

  3. Mertsj
    • 4 years ago
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    mridrik: Will someone please look at my last question, it has to deal with cubes and I need help from someone very smart.

  4. anonymous
    • 4 years ago
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    we want to see if \[x\oplus y=y\oplus x\]so don't be confused by this, just go right to the definition and see if it is true or not. i.e. work from the definition of the operation

  5. anonymous
    • 4 years ago
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    the left hand side of \[x\oplus y \] is \[x\oplus y = xy + x + y\] and the right hand side is \[y\oplus x = yx +y+x\] and now the question is are they equal? so we see that \[xy+x+y=yx+y+x\] because both multiplication and addition are commutative, and therfore \[x\oplus y = y\oplus x\]

  6. anonymous
    • 4 years ago
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    by the way it is clear ( i hope) that the symbol used is not important. it is just a definition for the operation. they could have used any symbol. i use \[\oplus\] but i could have use \[*\] or \[\heartsuit \] or anything

  7. anonymous
    • 4 years ago
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    ready for the next one?

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