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If a, b are real number,  two sets \(\displaystyle \{1,a+b,a\}\) and \(\left\{0,\frac{b}{a},b\right\}\)  What is b - a?

 Jun 23, 2020
 #1
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If the two sets are equal, that is, if they contain the same elements, then:

 

{1, a + b, a}     and     {0, b/a,  b}

 

The '0' of the second set cannot equal a becuase that would make the expression b/a undefined.

So  a + b  =  0   --->   a = -b.

If  1  =  b,  then  a  =  -1.

 

Let's see if this works:

The first set has:   1,  a + b  =  -1 + 1  =  0,  and  a = -1.

The second set has:    0,  b/a  =  1/-1  =  -1,  and  b = 1.

So, the first set does contain the same numbers as the second set.

 

Now, to find  b - a  =  1 - -1  =  1 + 1  =  2. 

 Jun 23, 2020

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