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 →

1.	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.
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.