Let the set 𝑨 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓} and B= {𝟑, 𝟒, 𝟓, 𝟔, 𝟕}. Find 𝑨⨁𝑩
Question
Let the set 𝑨 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓} and B= {𝟑, 𝟒, 𝟓, 𝟔, 𝟕}. Find 𝑨⨁𝑩
Solution
The operation ⨁ is not defined in the question. However, if we assume that ⨁ represents the symmetric difference of two sets, then we can proceed as follows:
The symmetric difference of two sets A and B is the set of elements which are in either of the sets and not in their intersection.
The intersection of A and B, denoted by A ∩ B, is {3, 4, 5}.
Now, let's find the elements that are in A but not in A ∩ B, and the elements that are in B but not in A ∩ B.
The elements in A but not in A ∩ B are {1, 2}.
The elements in B but not in A ∩ B are {6, 7}.
Therefore, the symmetric difference of A and B, denoted by A ⨁ B, is {1, 2, 6, 7}.
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