prof that if a=<b and d=<c is given than |a-c|=<|b-d| from the sum of the given we get a+d=<b+c that as far as i went
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That is not true. Take $\displaystyle a=1, b = 2, c=2, d=2$
If you leave off the magnitude signs, it is true. To prove that statement (without the magnitude signs), you could compare -c with -d.
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