Set Operations Calculator

About Set Operations Calculator

Union combines all elements, intersection finds common elements, difference finds elements in A but not B.

How to use this calculator

1. Enter the first set, for example \(A = \{1, 2, 3, 4\}\).
2. Enter the second set, for example \(B = \{3, 4, 5\}\).
3. Choose the operation you want, union \(A \cup B\), intersection \(A \cap B\), or difference \(A \setminus B\).
4. Read the result, which lists the elements in the new set.

The formula explained

The formulas \(A \cup B\), \(A \cap B\), and \(A \setminus B\) compute the union, intersection, and difference of two sets. Union combines all unique elements, intersection keeps only common elements, and difference keeps elements in the first set that are not in the second.

• A = the first set
• B = the second set
• \(\cup\) = union, all elements from either set without duplicates
• \(\cap\) = intersection, elements common to both sets
• \(\setminus\) = difference, elements in the first set but not in the second

Step by step method

1. List the elements in each set clearly, without repeating any element inside a set.
2. For union, collect every unique element that appears in either set.
3. For intersection, keep only the elements that appear in both sets.
4. For difference \(A \setminus B\), remove from \(A\) any elements that also appear in \(B\).

Worked example

Problem. Let \(A = \{1, 2, 3, 4\}\) and \(B = \{3, 4, 5\}\). Find \(A \cup B\), \(A \cap B\), and \(A \setminus B\).

1. Union: combine all unique elements from both sets, so \(A \cup B = \{1, 2, 3, 4, 5\}\).
2. Intersection: find the elements shared by both sets, so \(A \cap B = \{3, 4\}\).
3. Difference: keep elements in \(A\) that are not in \(B\), so \(A \setminus B = \{1, 2\}\).

Tips and common mistakes

• A set does not repeat elements, so write \(\{1, 1, 2\}\) as \(\{1, 2\}\).
• Be careful with difference, because \(A \setminus B\) is not the same as \(B \setminus A\).

Frequently asked questions