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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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!

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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ah you are checking to see if it is commutative. so lets do it
I've never studies that, that i recall, but its gonna be on my SAT
mridrik: Will someone please look at my last question, it has to deal with cubes and I need help from someone very smart.

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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
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 \[x\oplus y = y\oplus x\]
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
ready for the next one?

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