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Symmetric Difference Calculator

Work out symmetric difference instantly with clear inputs, formula shown and shareable results.

About Symmetric Difference Calculator

The symmetric difference contains the elements in exactly one of the two sets — the set-theoretic XOR. It equals the union minus the intersection, so |A △ B| = |A ∪ B| − |A ∩ B|.

Formula

Symmetric difference

A △ B = (A ∪ B) \\ (A ∩ B) = (A \\ B) ∪ (B \\ A)

Worked example

With the default values below, Symmetric Difference Calculator returns A △ B of 1, 2, 5, 6. Change any input above and every figure here is recalculated in your browser.

Inputs used

Set A
1, 2, 3, 4
Set B
3, 4, 5, 6

Results

A △ B
1, 2, 5, 6
|A △ B|
4
|A ∩ B|
2
|A ∪ B|
6

Step by step

  1. 1Values used
  2. 2Symmetric difference
  3. 3A △ B= 1, 2, 5, 6
  4. 4|A △ B|= 4
  5. 5|A ∩ B|= 2
  6. 6|A ∪ B|= 6

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For A = {1,2,3,4} and B = {3,4,5,6}?

A △ B = {1, 2, 5, 6}, of size 6 − 2 = 4.

Why is it like XOR?

Membership in A △ B is true when membership in exactly one of A and B is true, which is exactly the XOR truth table.

Related Calculators

Symmetric Difference Calculator – Calculate A △ B & |A △ B|