Set and Propositions - Part 2

Algebra Level 1

If a , b ∈ R \displaystyle a,b∈R , two sets { 1 , a + b , a } \displaystyle \{1,a+b,a\} and { 0 , b a , b } \displaystyle \left\{0,\frac{b}{a},b\right\} are equivalent.

What is b − a b-a ?


The answer is 2.

Alice Smith by Alice Smith , 20, China

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1 solution

Zee Ell
May 19, 2019

If the two sets {1, a + b, a} and {0, b/a, b} are equivalent, then their elements are the same (pairwise).

Hence, either a = 0 (which cannot be the case, since then b/a would be undefined) or a + b = 0, which gives us b = -a , a = b/a = -1 then b = 1 and the two equivalent sets {1, 0, -1} and {0, -1, 1}.

Therefore:

b − a = 1 − ( − 1 ) = 2 b - a = 1 - (-1) = \boxed {2}

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