prove that |a+b|=|a|+|b|

Question

prove that problem

Answer 1

There are four combinations of signs for a and b where the magnitudes are the same but the signs are + or -: a and b both positive; a positive and b negative; a negative and b positive; a and b both negative. 

Case 1: a=1, b=2, |a|+|b|=3=|a+b|

Case 2: a=1, b=-2, |a|+|b|=3, |a+b|=1

Case 3: a=2, b=-1, |a|+|b|=3, |a+b|=1

Case 4: a=-1, b=2, |a|+|b|=3, |a+b|=1

Case 5: a=-2, b=1, |a|+|b|=3, |a+b|=1

Case 6: a=-1, b=-2, |a|+|b|=3=|a+b|

So the proposition isn't true.