MAT 300 Mathematical Structures
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| Existential Instantiation | Introducing a new variable x into the proof to stand for an object for which P(x) is true. This means that you can now assume that P(x) is true
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| Universal Instantiation | You can plug in any value, say a, for x and use this given to conclude that P(a) is true.
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| m divides n (m|n) | n is evenly divisible by m
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| Odd integers |
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| Even integers |
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| Uniqueness (E!) |
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| Ordered pairs | Pairs of values in which the order of the values makes a difference (a, b)
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| First coordinate | The first value in an ordered pair, so a
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| Second coordinate | The second value in an ordered pair, so b
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| Cartesian product (AxB) of two sets | The set of all ordered airs in which the first coordinate is an element of A and the second is an element of B
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| Relations from A to B | Suppose A and B are sets. Then a set R (is a subset of) AxB is called a relation from A to B
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| Domain of relations and functions | p. 172
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| Range of relations and functions | p. 172
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| Inverse of relations | p. 172
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| Composition of relations and functions |
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| Identity relation and function (iA) on a set A |
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| Reflexive relations | p. 184-185
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| Symmetric relations | p. 184-185
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| Transitive relations | p. 184-185
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| Antisymmetric relations | p. 189
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| Partial orders | A relation R on a set A that is reflexive, transitive, and antisymmetric
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| Total orders | p. 190
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| Smallest element | p. 189-
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| Largest element |
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| Equivalence relations |
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| Equivalence classes |
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| Partitions |
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| A modulo R (A/R) |
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| Congruence modulo |
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| Functions f: A --> B |
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| Codomain of a function |
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