Intersection of Sets, Union of Sets and Venn Diagrams

Main ideas and lessons

• Intersection of two sets = the set of elements common to both sets.
• Union of two sets = the set of elements that are in either set (combine them), listing shared elements only once.
• Empty set (null set):
  • The intersection of any set with an empty set is empty.
  • The union of any set with an empty set is the original set.

Venn diagrams

• The overlapping region shows the intersection.
• The entire combined coverage of both circles shows the union.

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Methodology (step-by-step instructions)

A) How to find the intersection of two sets

1. Identify all elements in Set A.
2. Identify all elements in Set B.
3. Select only the elements that appear in both sets.
4. Write the result as the intersection set (no duplicates).

B) How to find the union of two sets

1. List all elements from Set A.
2. Add elements from Set B that are not already included.
3. If an element is in both sets, include it once.
4. (Often shown in ascending order for numbers or alphabet order for letters.)

C) How to represent intersection and union using a Venn diagram

1. Draw two circles: one labeled A, the other labeled B.
2. Place elements that belong only to A in the A-only region.
3. Place elements that belong only to B in the B-only region.
4. Place elements common to both A and B in the overlap region (this region is the intersection).
5. The union is represented by the full area covered by both circles (both regions together).

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Examples conveyed (with results)

Intersection examples

• Set A = {2, 4, 5, 6, 9}, Set B = {2, 3, 5, 6, 7, 9}
  • Intersection = {2, 5, 6, 9}
• Set C = {3, 4, 6, 7, 10}, Set D = {3, 6, 8, 9}
  • Intersection = {3, 6}
• Set F = {a, b, c, d, f, g, j}, Set G = {a, c, g, h, k}
  • Intersection = {a, c, g}
• Set J = {5, 7, 10, 11}, Set K = {2, 4, 8, 13}
  • Intersection = empty set (no common elements)
• Set R = {3, 4, 7, 10}, Set S = empty set
  • Intersection = empty set

Union examples

• Set A = {1, 2, 3, 4}, Set B = {3, 4, 5, 6}
  • Union = {1, 2, 3, 4, 5, 6}
• Set C = {3, 5, 9, 11, 13}, Set D = {2, 3, 6, 8, 12}
  • Union = {2, 3, 5, 6, 8, 9, 11, 12, 13} (written in ascending order)
• Set J = {a, c, d, e}, Set K = {a, b, f, e, g}
  • Union = {a, b, c, d, e, f, g}
• Set X = {2, 5, 8, 12}, Set Y = empty set
  • Union = {2, 5, 8, 12}

Intersection and union with Venn diagram (final example)

• Set A = {3, 4, 5, 7}
• Set B = {2, 4, 5, 8}
• Intersection (overlap) = {4, 5}
• Union (both circles combined) = {2, 3, 4, 5, 7, 8}

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Speakers / sources

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