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8 Cards in this Set
- Front
- Back
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Relation |
Given sets A and B, we say that R, which is a subset of A x B, is a relation from A to B. |
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Equivalence Relation |
A relation R on A x A is called an equivalence relation if it reflexive, symmetric, and transitive. |
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Equivalence Class |
Given an equivalence relation R on A x A, we define the equivalence class of a in A to be the set [a] = {b in A | aRb}. |
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Function |
Given the sets A and B, the relation R from A to B is said to be a function if for each a in A there exists a unique b in B such that aRb. |
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Injective |
Let f:A->B. We say that f is injective if for all a, a' in A we have that f (a)=f (a') implies a=a'. |
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Surjective |
Let f:A->B. We say that f is surjective if for all b in B there exists an a in A such that f (a)=b. |
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Right Inverse |
Let f:A->B be given. We say that g:B->A is a right Inverse of f if f (g (b))=b for all b in B. |
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Left Inverse |
Let f:A->B be given. We say that g:B->A is a left Inverse of f if g (f (a))=a for all a in A. |
