Discrete Structures20765 marksNumerical: remainder theorem polynomialClosure of Relations
Define reflexive closure and symmetric closure. Find the remainder when 4x2 - x + 3 is divided by x + 2 using remainder theorem.
Define reflexive closure and symmetric closure. Find the remainder when $4x^2 - x + 3$ is divided by x + 2 using remainder theorem. [5]
- Polynomial: $f(x) = 4x^2 - x + 3$ - Divisor: $x + 2$ --- The reflexive closure of a relation $R$ on a set $A$ is the smallest reflexive relation on $A$ that contains $R$. It is formed by adding all pairs $(a, a)$ for every $a \in A$ that are not already in $R$. $$R^{ref} = R \cup \Delta \quad ...