Chapter 9: Q46E (page 617)
To determine whether "the set \(\{ x + n\mid n \in Z\} \) for all \(x \in {(0,1)^{\prime \prime }}\) are the partitions of the set of real numbers.
The set is the partition of the set of real numbers.
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Draw the Hasse diagram for the greater than or equal to relation on \(\{ 0,1,2,3,4,5\} \).
Show that the relation \({\rm{R}}\) consisting of all pairs \((x,y)\) such that \(x\) and \(y\) are bit strings of length three or more that agree in their first three bits is an equivalence relation on the set of all bit strings of length three or more.
To draw the Hasse diagram for divisibility on the set \(\{ 1,2,4,8,16,32,64\} \).
To prove that the relation \(R\) on set \(A\) is anti-symmetric, if and only if \(R \cap {R^{ - 1}}\) is a subset of the diagonal relation \(\Delta = \{ (a,a)\mid a \in A\} \)
To determine for each of these relations on the set decide whether it is reflexive, whether it is symmetric, whether it is anti symmetric, and whether it is transitive .
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