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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 \( \{1, 2, 3, 4, 5, 6\} \) as \( R = \{(a, b) : b = a + 1\} \) is reflexive, symmetric, or transitive, we will analyze each property step by step. ### Step 1: Identify the elements of the relation \( R \) The relation \( R \) consists of pairs \( (a, b) \) such that \( b = a + 1 \). We will find all such pairs for \( a \) in the set \( \{1, 2, 3, 4, 5, 6\} \): - For \( a = 1 \), \( b = 2 \) → \( (1, 2) \) - For \( a = 2 \), \( b = 3 \) → \( (2, 3) \) ...
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