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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 \( R = \{(a, b) : a \leq b^3\} \) 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 \( (a, a) \) belongs to \( R \). This means we need to check if \( a \leq a^3 \) holds for all \( a \). 1. **Test with \( a = 1 \)**: - \( 1 \leq 1^3 \) → \( 1 \leq 1 \) (True) ...
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