We say a binary operation $^{}$ is associative when a $^{}$ (b $^{}$ c) = (a $^{}$ b) $^{}$ (a $^{}$ c)

True

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False

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Solution

The correct option is B
False

We say a binary operation $$ is associative if a $^{}$ (b $^{}$ c) = (a $^{}$ b) $^{*}$ c. So the given statement is false.

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We say a binary operation $^{*}$ is associative when a $^{*}$ (b $^{*}$ c) = (a $^{*}$ b) $^{*}$ (a $^{*}$ c)

Q. Consider the binary operations*: R × R → and o: R × R → R defined as and a o b = a , &mnForE; a , b ∈ R . Show that * is commutative but not associative, o is associative but not commutative. Further, show that &mnForE; a , b , c ∈ R , a *( b o c ) = ( a * b ) o ( a * c ). [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over *? Justify your answer.

Consider the binary operations*: R ×R → and o: R × R → R defined as and a o b = a, &mnForE;a, b ∈ R. Show that * is commutative but not associative, o is associative but not commutative. Further, show that &mnForE;a, b, c ∈ R, a*(b o c) = (a * b) o (a * c). [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over *? Justify your answer.