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Check whether the relation R in R define...

Check whether the relation R in R defined by `R={(a ,b):alt=b^3}`is reflexive, symmetric or transitive.

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To determine whether the relation \( R = \{(a, b) : a < b^3\} \) 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 the set, the pair \( (a, a) \) is in \( R \). For our relation: - We need to check if \( a < a^3 \) for all \( a \). - This inequality can be rewritten as \( a^3 - a > 0 \). ...
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