Question

h. The statements A+B = C, A + C = B, and B +C = A are equivalent to each other. [Suggestion: Assume that A+B=C. Then "add" (B+C) to both sides of the equation giving (A+B)+(B+C) = C+(B+C). Then use parts (g) and (a) of this exercise.]

Answer 1

part g ---> http://math.stackexchange.com/questions/660468/prove-a-bc-bac-c-ab-using-the-definition-of-ab

part a ---> http://math.stackexchange.com/questions/660230/prove-a-emptyset-a-aa-emptyset-and-a-a-u-using-the-definition

Answer 2

So, I guess from what I've seen I should use the \[A+B\] definition and then use whatever I obtained from G and A to prove that all of those simple tiny problems are related to each other

Answer 3

@TuringTest @wio @perl @ikram002p

Answer 4

\[ A+B = C\]
\[ (A+B)+(B+C) = C+(B+C)\]

Answer 5

\[A+B=(A \cup B) \backslash (A \cap B)\]

Answer 6

\[$B+C=(B \cup C) \backslash (B \cap B)$.\]

Answer 7

\[(A \cup B) \backslash (A \cap B) + (B \cup C) \backslash (B \cap C) = C + (B \cup C) \backslash (B \cap C)\]

Answer 8

all those all up .. you will get
2(A+B+C) = (A+B+C)
which implies A, B or C is null set or ... they all are same and two same elements do not exists in a set.