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Show that the relation R in R defined as...

Show that the relation R in R defined as `R={(a ,b): alt=b}`, is reflexive and transitive but not symmetric.

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To show that the relation \( R \) defined as \( R = \{(a, b) : b = a + 1\} \) is reflexive, transitive, but not symmetric, we will analyze each property step by step. ### Step 1: Check Reflexivity A relation \( R \) is reflexive if for every element \( a \) in the set, the pair \( (a, a) \) is in \( R \). - For our relation \( R \), we need to check if \( (a, a) \) is in \( R \). - This means we need \( a = a + 1 \) for some \( a \). - However, this is not possible because there is no real number \( a \) such that \( a = a + 1 \). ...
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