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To show that ( A \oplus B = (A \cup B) - (A \cap B) ), we need to prove two inclusions.
For the first inclusion, let ( x \in A \oplus B ). This means that ( x ) is in exactly one of ( A ) or ( B ), but not both. Therefore, ( x ) is in ( A ) or ( B ), but not in their intersection. Hence, ( x \in (A \cup B) - (A \cap B) ).
For the second inclusion, let ( x \in (A \cup B) - (A \cap B) ). This means that ( x ) is in either ( A ) or ( B ), but not in their intersection. Thus, ( x ) is in exactly one of ( A ) or ( B ), leading to ( x \in A \oplus B ).
Therefore, we have shown that ( A \oplus B = (A \cup B) - (A \cap B) ).
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all major intersection have various other signs offering information to road users
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