Determine whether each relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes. Ibegin(enumerate [label=(\alph")] \ item The domain is a group of people. Ferson Zjis related to person yunder relation Mlif zland yhave the same favorite color. You can assume that there is at least one pair in the group, Aand y such that zMy %Enter your answer below this comment line. |item The domain is the set of all integers. ZEif I+is even. Arn integer ais even if z= 24for some integer 411 %Enter vour answer below this comment line.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 8

Determine whether each relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes.

1. The domain is a group of people. Person \( x \) is related to person \( y \) under relation \( M \) if \( x \) and \( y \) have the same favorite color. You can assume that there is at least one pair in the group, \( x \) and \( y \), such that \( x M y \).

   Enter your answer below this comment line.

2. The domain is the set of all integers. \( x M y \) if \( x + y \) is even. An integer \( x \) is even if \( x = 2k \) for some integer \( k \).

   Enter your answer below this comment line.

\end{enumerate}
Transcribed Image Text:Problem 8 Determine whether each relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes. 1. The domain is a group of people. Person \( x \) is related to person \( y \) under relation \( M \) if \( x \) and \( y \) have the same favorite color. You can assume that there is at least one pair in the group, \( x \) and \( y \), such that \( x M y \). Enter your answer below this comment line. 2. The domain is the set of all integers. \( x M y \) if \( x + y \) is even. An integer \( x \) is even if \( x = 2k \) for some integer \( k \). Enter your answer below this comment line. \end{enumerate}
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