Question on Absolute Value & Union/Intersection

[sushi]

Hey there.

Can someone please help me out here...how to solve..?

|x-1| = |x-1|

I know the next step is so get rid of the absolute values so

x-1 = x-1
but then the answer will be 0??? is it correct or..??




another question:
Let A={1,3,5,7,9} and B={2,4,6,8}, C={1,2,3,4,5}

whats the answer to..

A u B n C

p.s. u: union, n:intersection

could it be {1,2,3,4,5,6,7,8,9} or {2,4} ??

Thank you in advanceeee

[Dross]

Any and every x is a solution to |x-1|=|x-1|, not just zero.

As for your A u B n C Question - you get different answers depending on which operation you do first. For example:

(A u B) n C = ({1,3,5,7,9} u {2,4,6,8}) n {1,2,3,4,5}

= {1,2,3,4,5,6,7,8,9} n {1,2,3,4,5}

= {1,2,3,4,5}


...but...


A u (B n C) = {1,3,5,7,9} u ({2,4,6,8} n {1,2,3,4,5})

= {1,3,5,7,9} u {2,4}

= {1,2,3,4,5,7,9}


If brackets have been omited... I dunnow? Has a precedent like "do unions first" or "do the operation on the left first" been given to you? If not, the question would appear to be ambiguous...

[sushi]

Thanks Dross for replying I really appreciate it

btw urm, I still dont get why any and every x is a solution to |x-1| = |x-1| how is that possible?

[timeshifter]

Just start picking and choosing values of x to prove it.

x=5
|x-1|=|x-1|
|5-1|=|5-1|
|4|=|4|
4=4

Like that. No matter what value you put for x, you'll always come out with a solution that's true.