Let A={1,2,3,4} and let R, S, T, and U be the following relations: R={(1,1),(1,2),(1,3),(1,4)} S={(1,1),(2,1),(3,1),(4,1)} T={(1,2),(3,4),(4,1)} U={(2,1),(4,4),(3,1),(2,3)} For each of R, S, T, and U determine whether they are reflexive, symmetric or transitive and determine whether the given relations in A is an equivalence relation or not.
Let A={1,2,3,4} and let R, S, T, and U be the following relations: R={(1,1),(1,2),(1,3),(1,4)} S={(1,1),(2,1),(3,1),(4,1)} T={(1,2),(3,4),(4,1)} U={(2,1),(4,4),(3,1),(2,3)} For each of R, S, T, and U determine whether they are reflexive, symmetric or transitive and determine whether the given relations in A is an equivalence relation or not.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A={1,2,3,4} and let R, S, T, and U be the following relations:
R={(1,1),(1,2),(1,3),(1,4)}
S={(1,1),(2,1),(3,1),(4,1)}
T={(1,2),(3,4),(4,1)}
U={(2,1),(4,4),(3,1),(2,3)}
For each of R, S, T, and U determine whether they are reflexive, symmetric or transitive and determine whether the given relations in A is an equivalence relation or not.
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