सिद्ध कीजिए कि `** R xx R to R , (a, b) to a + 5b^3` द्वारा प्रदत्त एक द्विआधारी संक्रिया है।
(यहाँ `a ** b = a +5b^3,a, b in R` )

Show that * : R xx R to R defined by: a * b =a-5b is not abelian.

Show that * : R xx R to R defined by: a * b =a-5b is not abelian.

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 *: R xx R rarr R given by (a,b) rarr a + 4b^(2) is a binary operation compute (-5 ) *(2*0) .

Consider the binary operation * : R xx R rarr R and o : R xx R rarr R defined as a * b = |a-b| and a o b = a, AA a, b in R . Is o distributive over * ? Justify your answer.

The binary opertion ** R xx R to R is defined by a ** b = 2a + b. find (2 ** 3) **4.

Show that vv : R xx R rarr R given by (a, b) rarr max. [a, b) and ^^: R xx R rarr R given by (a, b) rarr min (a, b) are binary operations.

Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and the * : R xx R rarr R given by (a, b) rarr min {a , b} are binary operations.