Definition:Induced Operation

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Induced Operation may refer to:

$A \circ_\mathcal P B = \set {a \circ b: a \in A, b \in B}$

$\eqclass x \RR \circ_\RR \eqclass y \RR = \eqclass {x \circ y} \RR$

$\tuple {s_1, s_2, \dotsc, s_n} \circ \tuple {t_1, t_2, \dotsc, t_n} := \tuple {s_1 \circ_1 t_1, s_2 \circ_2 t_2, \dotsc, s_n \circ_n t_n}$ for all ordered $n$-tuples in $S$

$f \oplus g: S \to T: \forall x \in S: \map {\paren {f \oplus g} } x = \map f x \circ \map g x$