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A = { 1, 5, 6, 8 } B = { 1, 6, 7 } C = { 2, 4, 7 } A ⊕ ( C - B ) = { }

 Apr 28, 2022
 #2
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What is the definition of \(\oplus\) here?

 Apr 29, 2022
 #3
avatar+9277 
+2

Since you didn't reply, I will assume that it denotes the symmetric difference \(A \oplus B = (A \cup B) - (A \cap B)\).

 

First, \(C - B\) is just the collection of elements in C that is not in B, i.e., \(C - B = \{2, 4\}\).

Now, we calculate \(A \oplus (C - B) = A \oplus \{2 ,4\}\).

Note that \(A \cap \{2, 4\} = \varnothing\) since the two sets do not have common elements. Then \(A \oplus \{2, 4\} = A \cup \{2, 4\} = \{1,2,4,5,6,8\}\).

 

Hence, we have \(A \oplus (C - B) = \{1,2,4,5,6,8\}\).

MaxWong  May 2, 2022
edited by MaxWong  May 2, 2022

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