For any two real numbers, an operation `**` defined by `a**b=1+ab` is

On the set Q of all rational numbers an operation * is defined by a*b=1+ab. show that * is a binary operation on Q.

On the set Q of all rational numbers if a binary operation * is defined by a*b=(ab)/(5), prove that * is associative on Q.

On the set Q^(+) of all positive rational numbers a binary operation * is defined by a*b=(ab)/(2) for all a,b in Q^(+). The inverse of 8 is (1)/(8) (b) (1)/(2)(cc)2(d)4

Q^(+) is the set of all positive rational numbers with the binary operation * defined by a*b=(ab)/(2) for all a,b in Q^(+). The inverse of an element a in Q^(+) is a (b) (1)/(a)( c) (2)/(a) (d) (4)/(a)

Find the identity element in set Q^(+) of all positive rational numbers for the operation * defined by a^(*)b=(ab)/(2) for all a,b in Q^(+)

Let Z be the set of all integers, then , the operation * on Z defined by a*b=a+b-ab is

For any two real numbers a and b,we define a R b if and only if sin^(2)a+cos^(2)b=1. The relation R is

Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

On the set Z of integers a binary operation * is defined by a*b=ab+1 for all a,b in Z Prove that * is not associative on Z