Chapter 9: Q1RE (page 634)
How many relations are there on a set with \(n\) elements?
There are \({2^{{n^2}}}\) relations on a set \(S\) with \(n\) elements.
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To find the ordered pairs \((a,b)\) in \({R^2}\;\& \;\;{R^n}\) relation where \(n\) is a positive integer.
Show that the relation \(R\) on a set \(A\) is antisymmetric if and only if \(R \cap {R^{ - 1}}\) is a subset of the diagonal relation \(\Delta = \{ (a,a)\mid a \in A\} \).
Whether there is a path in the directed graph in Exercise 16 beginning at the first vertex given and ending at the second vertex given.
How can the directed graph representing the reflexive closure of a relation on a finite set be constructed from the directed graph of the relation?
To determine whether the relation on the set of all real numbers is reflexive, symmetric, anti symmetric, transitive, where if and only ifx=1 or y=1.
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