Symmetric difference: Difference between revisions

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Given two [[set]]s ''A'' and ''B'', ~~where~~ ''A'' ~~contains:~~

;Task

* John

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Given two [[set]]s ''A'' and ''B'', compute <math>(A \setminus B) \cup (B \setminus A).</math>

* Bob

* Mary

* Serena

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That is, enumerate the items that are in ''A'' or ''B'' but not both. This set is called the [[wp:Symmetric difference|symmetric difference]] of ''A'' and ''B''.

and ''B'' contains:

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In other words: <math>(A \cup B) \setminus (A \cap B)</math> (the set of items that are in at least one of ''A'' or ''B'' minus the set of items that are in both ''A'' and ''B'').

* Jim

* Mary

* John

* Bob

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Optionally, give the individual differences (<math>A \setminus B</math> and <math>B \setminus A</math>) as well.

compute

:<math>(A \setminus B) \cup (B \setminus A).</math>

;Test cases

⚫

That is, enumerate the items that are in ''A'' or ''B'' but not both. This set is called the [[wp:Symmetric difference|symmetric difference]] of ''A'' and ''B''.

A = {John, Bob, Mary, Serena}

B = {Jim, Mary, John, Bob}

⚫

In other words: <math>(A \cup B) \setminus (A \cap B)</math> (the set of items that are in at least one of ''A'' or ''B'' minus the set of items that are in both ''A'' and ''B'').

⚫

Optionally, give the individual differences (<math>A \setminus B</math> and <math>B \setminus A</math>) as well.

;Notes

# If your code uses lists of items to represent sets then ensure duplicate items in lists are correctly handled. For example two lists representing sets of <code>a = ["John", "Serena", "Bob", "Mary", "Serena"]</code> and <code>b = ["Jim", "Mary", "John", "Jim", "Bob"]</code> should produce the result of just two strings: <code>["Serena", "Jim"]</code>, in any order.

# In the mathematical notation above <code>A \ B</code> gives the set of items in A that are not in B; <code>A ∪ B</code> gives the set of items in both A and B, (their ''union''); and <code>A ∩ B</code> gives the set of items that are in both A and B (their ''intersection'').

=={{header|Ada}}==

Ada has the lattice operation '''xor''' predefined on Boolean, modular types, 1D arrays, set implementations from the standard library. The provided solution uses arrays: