Give a binary relation R on an n-element set such that R != ∅ and |R ◦ R^(−1) | = n^(2) · |R^(−1) ◦ R
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Give a binary relation R on an n-element set such that R != ∅ and |R ◦ R^(−1) | = n^(2) · |R^(−1) ◦ R|
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- a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the equivalence class [ 3 ]. b. Let R be the equivalence relation congruence modulo 4 that is defined on Z in Example 4. For this R, list five members of equivalence class [ 7 ].Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.How many equivalence relations on the set {1, 2, 3}?
- Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have the same cardinality?Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on theset {1, 2, 3, 4} that is reflexive, symmetric and transitive.Find the number of all onto functions from the set {1, 2, 3, ... , n} to itself.
- Which of these relations on {0, 1, 2, 3} are equivalence relations? *count the number of possible equivalence relations on a set of size n by providing a formula in terms of n (and prove it works)on the set of real numbers x^2 + y^2 =1 what binary relation is that? Please provide detail explanation. Help me.I will give upvote.