let A, B and C be on empty sets such that A delta B is equal to C. The...
A Delta B
To understand the given statement, let's first define the symmetric difference between two sets. The symmetric difference, denoted by A delta B, between two sets A and B is the set of elements that are in either A or B, but not in both.
Empty Sets
An empty set, also known as the null set, is a set that contains no elements. It is denoted by the symbol Ø or {}.
Given Information
We are given three empty sets A, B, and C, and it is stated that the symmetric difference between sets A and B is equal to set C.
Explanation
Since A and B are empty sets, they do not contain any elements. Therefore, the symmetric difference between A and B, denoted as A delta B, will also be an empty set. This is because there are no elements that are in either A or B, but not in both.
So, A delta B = Ø (empty set)
According to the given information, A delta B = C. Since A delta B is an empty set, C must also be an empty set.
Therefore, C = Ø (empty set)
Conclusion
In conclusion, if A, B, and C are all empty sets and the symmetric difference between sets A and B is equal to set C, then C must also be an empty set.
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