Set operations
Membership and inclusion, the empty set, defining a set by listing or by a property, union, intersection, difference, symmetric difference, complement, Venn diagrams and De Morgan's laws.
- 28 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
- Understand
A few cards from the deck
Inclusion: what is it?
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Relation between two sets A and B that holds when every element of A is also an element of B: written A ⊂ B.
∈ links an element to a set, ⊂ links two sets: 2 ∈ {1, 2}, but {2} ⊂ {1, 2}.
A = {1, 2, 3} and B = {3, 4}. What is A ∖ B?
{1, 2}{1, 2, 4}{3}{4}
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{1, 2}A ∖ B keeps the elements of A that are not in B: 3 is removed. The 4 belongs to B only, so it is not in A ∖ B.
The empty set, written …, has no element; it is a … of every set.
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The empty set, written ∅, has no element; it is a subset of every set.
For ∅ ⊂ A to fail, some element of ∅ would have to be missing from A: there is none. Careful, ∅ is not an element of every set.
Symmetric difference: what is it?
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The set of elements that lie in exactly one of the two sets, written A Δ B.
A Δ B = (A ∖ B) ∪ (B ∖ A) = (A ∪ B) ∖ (A ∩ B). With A = {1, 2, 3} and B = {3, 4}, the result is {1, 2, 4}.