Find the identity element in the set `I^+` of all positive integers defined by a*b=`a+b` for all `a ,\ b in I^+` .

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

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

Find the identity element in the set of all rational numbers except -1 with respect to * defined by a*b= a+b+a b .

Let * be a binary operation on the set Q_0 of all non-zero rational numbers defined by a*b= (a b)/2 , for all a ,\ b in Q_0 . Show that (i) * is both commutative and associative (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

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

Q^+ is the set of all positive rational numbers with the binary operation * defined by a*b= (a b)/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

On the set W of all non-negative integers * is defined by a*b=a^b . Prove that * is not a binary operation on Wdot

Find the identity and invertible elements in Z of the binary operation * defined as a * b = a + b-4, AA a, b in Z .

Let '*' be a binary operation on Q_0 (set of all non-zero rational numbers) defined by a*b=(a b)/4 for all a , b in Q_0dot Then, find the identity element in Q_0 inverse of an element in Q_0dot

Let '*' be a binary operation on Q_0 (set of all non-zero rational numbers) defined by a*b=(a b)/4 for all a , b in Q_0dot Then, find the identity element in Q_0 inverse of an element in Q_0dot