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eduhilfe
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Asked: 2020-10-05T22:27:04+01:00 In:

12. Consider the binary operations\ast : R\times R \to R and \circ : R\times R \to R defined as a \ast b =|a-b| and a \circ b = a, \forall a,b \in R . Show that * is commutative but not associative, o is associative but not commutative. Further, show that \forall a, b, c \in R \; , a\ast (b \circ c) = (a\ast b) \circ (a\ast b) . [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over * ? Justify your answer.

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12. Consider the binary operations\ast : R\times R \to R and \circ : R\times R \to R defined as a \ast b =|a-b| and a \circ b = a, \forall a,b \in R . Show that * is commutative but not associative, o is associative but not commutative. Further, show that \forall a, b, c \in R \; , a\ast (b \circ c) = (a\ast b) \circ (a\ast b) . [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over * ? Justify your answer.
miscellaneous-ch-1 (ncert class 12th maths)ncertrelations and functions
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