MathematicsChapter 3: Sets and Relations
Subset Disjoint Venn
A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
Learning objectives
- Explain Subset Disjoint Venn in simple mathematical language.
- Apply subset correctly.
- Apply disjoint, overlapping, venn correctly.
- Use the symbols, conditions, and formulae accurately.
- Solve a short example and check the answer.
- Recognise and correct common mistakes.
Definition
A is a subset of B when every element of A is also an element of B (written A <= B or A subset B). Two sets are disjoint if their intersection is empty; they are overlapping if they share at least one element. A Venn diagram draws the universe U as a rectangle and the sets as regions inside it, usually overlapping circles. The picture does not prove a law, but it stops you mixing union with intersection.
Where / symbols
- subset
- A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
- disjoint
- Two sets are disjoint if their intersection is empty; they are overlapping if they share at least one element.
- overlapping
- Two sets are disjoint if their intersection is empty; they are overlapping if they share at least one element.
- Venn
- A Venn diagram draws the universe U as a rectangle and the sets as regions inside it, usually overlapping circles.
- U
- A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
- rectangle
- A Venn diagram draws the universe U as a rectangle and the sets as regions inside it, usually overlapping circles.
- Subset
- A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
- Disjoint
- Two sets are disjoint if their intersection is empty; they are overlapping if they share at least one element.
- intersection empty
- Disjoint means intersection empty, not 'drawn far apart for art.
- proper subset
- Proper subset means A is inside B but A is not equal to B.
Overview
Containment, then how two blobs can sit:
Subset
A is a subset of B if membership in A forces membership in B. Every set is a subset of itself. The empty set is a subset of every set. Proper subset means A is inside B but A is not equal to B. N is a subset of W, W of Z, Z of Q, Q of R.
Examples {1, 2} subset {1, 2, 3} · N subset W subset Z · {} subset {5}
Disjoint, Overlapping, Venn
Disjoint sets share nothing: A intersect B is empty. Overlapping sets share something. In a Venn diagram, U is the rectangle; circles inside show A and B. The lens (overlap) is the intersection. The full two-circle blob is the union. The region in the rectangle outside A is the complement A'.
Examples {1, 2} and {3, 4} are disjoint · {1, 2} and {2, 3} overlap at 2 · U drawn as a rectangle around the circles
WHAT — Core idea
A is a subset of B when every element of A is also an element of B (written A <= B or A subset B). Two sets are disjoint if their intersection is empty; they are overlapping if they share at least one element. A Venn diagram draws the universe U as a rectangle and the sets as regions inside it, usually overlapping circles. The picture does not prove a law, but it stops you mixing union with intersection.
WHY — Why it matters
Subset is about containment, not about size alone: a smaller-looking roster can fail to be a subset if it contains a stray element. Disjoint is stronger than 'different'; two different sets can still overlap.
HOW — Method and examples
1. SUBSET: A is a subset of B if membership in A forces membership in B. 2. DISJOINT, OVERLAPPING, VENN: Disjoint sets share nothing: A intersect B is empty.
HOW — Answer in an exam
U is a rectangle in the usual school Venn picture, not a circle. Disjoint means intersection empty, not 'drawn far apart for art.' A subset may equal the parent set; say proper subset if you need strict inside.
Explanation
Subset is about containment, not about size alone: a smaller-looking roster can fail to be a subset if it contains a stray element. Disjoint is stronger than 'different'; two different sets can still overlap.
In simple words
U is a rectangle in the usual school Venn picture, not a circle. Disjoint means intersection empty, not 'drawn far apart for art.' A subset may equal the parent set; say proper subset if you need strict inside.
Key points
- subset
- disjoint
- overlapping
- Venn
- empty set
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Subset Disjoint Venn
Sticky Notes · Quick Revision
WHAT
- A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
Key Points
- A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
- A is a subset of B if membership in A forces membership in B.
- Disjoint sets share nothing: A intersect B is empty.
- Subset is about containment, not about size alone: a smaller-looking roster can fail to be a subset if it contains a stray element.
HOW
- 1. SUBSET: A is a subset of B if membership in A forces membership in B.
- 2. DISJOINT, OVERLAPPING, VENN: Disjoint sets share nothing: A intersect B is empty.
Examples
- {1, 2} subset {1, 2, 3}
- N subset W subset Z
- {} subset {5}
- {1, 2} and {3, 4} are disjoint
- {1, 2} and {2, 3} overlap at 2
Common Mistake
- U is a rectangle in the usual school Venn picture, not a circle.
- Disjoint means intersection empty, not 'drawn far apart for art.
Exam Tip
- U is a rectangle in the usual school Venn picture, not a circle. Disjoint means intersection empty, not 'drawn far apart for art.' A subset may equal the parent set; say proper subset if you need strict inside.
60-second revision
- A is a subset of B when every element of A is also an element of B (written A <= B or A subset B).
- A is a subset of B if membership in A forces membership in B.
- Disjoint sets share nothing: A intersect B is empty.
- Subset is about containment, not about size alone: a smaller-looking roster can fail to be a subset if it contains a stray element.
- U is a rectangle in the usual school Venn picture, not a circle.
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