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Chapter 9: Q2RE (page 634)

What is a transitive relation?

Short Answer

Expert verified

The transitive relation is defined.

Step by step solution

01

Given data

A relation.

02

Concept used relation

A relation between two sets is a collection of ordered pairs containing one object from each set.

03

Define relation

In mathematics, a binary relation \({\rm{R}}\) over a set \({\rm{X}}\) is transitive if whenever an element \(a\) is related to an element \(b\) and \(b\) is related to an element \(c\) then \(a\) is also related to \(c\). In symbolic form, \(\forall a,b,c \in X:(aRb \wedge bRc) \Rightarrow aRc\).

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Most popular questions from this chapter

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 determine an example of an irreflexive relation on the set of all people.

Draw the Hasse diagram for inclusion on the set \(P(S)\) where \(S = \{ a,b,c,d\} \).

Show that if \(R\) and \(S\) are both \(n\)-ary relations, then

\({P_{{i_1},{i_2}, \ldots ,{i_m}}}(R \cup S) = {P_{{i_1},{i_2}, \ldots ,{i_m}}}(R) \cup {P_{{i_1},{i_2}, \ldots ,{i_m}}}(S)\).

To draw the Hasse diagram for divisibility on the set \(\{ 1,2,4,8,16,32,64\} \).
See all solutions

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