द्विआधारी संक्रियाओं `**: R xxtoR ` तथा `o:R xxR to R ` निम्न प्रकार परिभाषित है
` a**b =[ a-b | ` तथा ` aob =a AA a,b inR ` सिद्ध कीजिए की `a**(boc ) = (a**b) o ( a**c) AAa,b,c in R `

Consider the binary opertions **: R xx R to R and o : R xx R to R defined as a ** b = |a -b| and a o b =a, AA a, b in R. Show that ** is commutative but not associative, o is associative but not commutative. Further, show that AA a,b,c in R, a ** (b o c) = (a**b) o (a **c). [If it is so, we say that the opertion ** distributes over the opertion 0]. Does o distribute over ** ? Justify your answer.

Consider the binary operation **:R xxR to R and o:R xx R to R defined as a**b = |a-b| and a o b = a . For all a , b in R . Show that * is commutative but not associative, .o. is associative but not commutative.

Consider the binary operations * : R xx R to R and o: R xx R to R defined as a * b = |a-b| and a o b = a for all a,b in R . Show that '*' is commutative but not associative, 'o' is associative but not commutative.

Let A = (a,b,c) and R = (a,a), (b,b), (c,c), (b,c), (a,b) be a relation on A, then R is

Let R be a relation on A = {a, b, c} such that R = {(a, a), (b, b), (c, c)}, then R is

Let R be a relation on A = {a, b, c} such that R = {(a, a), (b, b), (c, c)}, then R is

Consider the binary operations ""^(**):RxxRtoR and o:RxxR defined by a^(**)b=|a-b| aob=a, AA a,b in R Examine, if o distributes over ""^(**) .