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37 Cards in this Set
- Front
- Back
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What does this symbol ( ∈ ) mean? |
Is an element of |
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What does this symbol ( ∉ ) mean? |
Is not an element of |
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A = {1, 2, 3, 4, 5, 6, 7} - 5 ∈ A ? |
Yes, 5 ∈ A |
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What set of numbers does this symbol (ℤ) represent? |
ℤ represents Integers |
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What set of numbers does this symbol (ℕ) represent? |
ℕ represents natural numbers (non-negative integers) |
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What set of numbers does this symbol (ℝ) represent? |
ℝ represents real numbers |
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Write out the following set using set builder notation: A = {1, 2, 3, 4, 5, 6, 7} |
A = { x ∈ ℤ | 1 <= x <= 7 } |
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A = { x ∈ ℤ | x = 2k for k = 1,2,3,...,20 }. Express this in list method |
A = { 2, 4, 6, 8,..., 40 } |
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When are two sets equal? |
When two sets have exactly the same members |
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P = { 1, 3, 1, 1, 4, 3}, Q = { 1, 3, 4 }. Does P = Q? |
Yes, sets P and Q are equal |
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Should elements of sets be repeated? |
No, repetition is unnecessary. Any duplicate elements can be removed. |
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Is this a valid set? A = {ℤ, ℤ+, ℕ, ℝ} |
Yes. Sets can contain sets as elements. |
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What does this symbol ( ∅ ) represent? |
The null set. Also known as the empty set. |
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Are { ∅ } and ∅ equivalent? |
No |
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What does this symbol ( ⊆ ) represent? |
⊆ is the subset symbol (eg: A ⊆ B means that A is a subset of B)
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When is A a subset of B? |
A is a subset of B when each element in A is also an element of B |
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X = { 1, 2, 3, 4, 5, 6, 7 }, Y = { 1, 3, 5, 7 }. Y ⊆ X ? |
Yes, Y ⊆ X because all each element within Y is also an element in X. |
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When is A a proper subset of B? |
A is a proper subset of B when A ⊆ B AND A ≠ B. |
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What does this symbol ( ⊂ ) mean? |
Proper subset (eg: A ⊂ B) |
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What does this symbol represent ( |A| ) ? |
Cardinality of set A |
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What is the cardinality of a set? |
The number of elements within it |
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For any set A, is A ⊆ A? |
Yes. A ⊆ A as each element of A is also in A. |
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For any set A, is ∅ ⊆ A? |
Yes. Each element in the null set is also in set A, even though technically there aren't any elements in the null set. |
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For any set A, is A ⊂ A? |
No. For a set to be a proper subset, it cannot equal the original set. |
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For any set A, is ∅ ⊂ A? |
Yes. As long as set A is not empty, then ∅ ⊂ A because all elements of ∅ are in set A, but ∅ is not equal to set A. |
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What is | ∅ | ? |
This is the cardinality of the null set. The null set contains no elements, so | ∅ | = 0. |
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X = {x ∈ ℤ+ | x is even and x < 200}. What is |X|? |
Count only even numbers while x < 200. |X| = 99. |X| is not 100 because we don't count 200. |
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What is a power set? |
A power set is a set which contains all subsets of that set. |
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What does P(A) denote? |
The power set of set A |
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B = {1, 2, 3}. What is P(B) ? |
P(B) = { ∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} } |
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What is the cartesian product of a pair of sets A and B? |
The cartesian product of a pair of sets A and B is a set of ordered pairs (a, b) where a ∈ A and b ∈ B. |
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A × B = { (a, b) | a ∈ A and b ∈ B} - what is this notation representing? |
The cartesian product of sets A and B. |
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What is an ordered n-tuple? |
A list of n elements which can be written as such: (a, b, c, d, ...) |
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A = {1, 2, 3}, C = {p, q}. What is A X C? |
A X C = { (1, p), (2, p), (3, p), (1, q), (2, q), (3, q) } |
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What does this symbol ( ⋃ ) represent? |
The union of two sets. Same as OR in boolean logic. |
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What does this symbol ( ⋂ ) represent? |
The intersection of two sets. Same as AND in boolean logic |
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What does this symbol ( ' ) represent? |
The complement of a set. Same as NOT in boolean logic |
