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Check whether the relation R defined in ...

Check whether the relation `R` defined in the set `{1, 2, 3, 4, 5, 6}`as `R = {(a , b) : b = a + 1}`is reflexive, symmetric or transitive.

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To determine whether the relation \( R \) defined on the set \( A = \{1, 2, 3, 4, 5, 6\} \) as \( R = \{(a, b) : b = a + 1\} \) is reflexive, symmetric, or transitive, we will analyze each property step by step. ### Step 1: Check for Reflexivity A relation \( R \) is reflexive if for every element \( a \in A \), the pair \( (a, a) \) is in \( R \). - For \( a = 1 \), \( (1, 1) \) is not in \( R \) because \( b \) must equal \( a + 1 \) (which would be 2). - For \( a = 2 \), \( (2, 2) \) is not in \( R \). - For \( a = 3 \), \( (3, 3) \) is not in \( R \). ...
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