🦭 Number Sets (ℕ, ℤ, ℚ, ℝ)
Master union and intersection of sets with step-by-step guidance and interactive exercises.
Union & Intersection
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Find the resulting set of the union (∪) or intersection (∩) of the two sets below. Write the numbers inside curly braces separated by commas, e.g. {1, 2, 3}, or type ∅ for the empty set.
Learning Topics
Set Operations: Union (∪) & Intersection (∩)
We can combine two sets using two key operations:
• ∪ (Union) — "everything together": The union
Example:
• ∩ (Intersection) — "what they share": The intersection
Example:
• ∅ (Empty Set): When two sets share nothing, their intersection is the empty set ∅.
Example:
Tip: Union = more (or equal) elements. Intersection = fewer (or equal) elements.
• ∪ (Union) — "everything together": The union
A ∪ B contains all elements that appear in A, in B, or in both. Think of it as merging two groups.Example:
{1, 2, 3} ∪ {3, 4, 5} = {1, 2, 3, 4, 5} (no duplicates!)• ∩ (Intersection) — "what they share": The intersection
A ∩ B contains only the elements that appear in both A and B. Think of it as the overlap.Example:
{1, 2, 3} ∩ {3, 4, 5} = {3} (only 3 is in both)• ∅ (Empty Set): When two sets share nothing, their intersection is the empty set ∅.
Example:
{1, 2} ∩ {3, 4} = ∅Tip: Union = more (or equal) elements. Intersection = fewer (or equal) elements.
Learning Topics
Frequently Asked Questions
What is a set and what are its elements?
A set is a collection of distinct objects or numbers, which are called elements or members. We write a set by listing its elements inside curly braces, like A = {1, 2, 3}. In this set, 1, 2, and 3 are the elements.
What do the symbols ∈ and ∉ mean?
The symbol ∈ means "belongs to" or "is an element of" (for example, 2 ∈ {1, 2, 3} is true). The symbol ∉ means "does not belong to" or "is not an element of" (for example, 4 ∉ {1, 2, 3} is true).
What is the difference between union (∪) and intersection (∩)?
The union (A ∪ B) combines all elements from both sets into a new set. The intersection (A ∩ B) contains only the elements that are present in both sets at the same time.