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 .

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

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 * 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 .

Find the identity element of the binary operation ** on ZZ defined by a**b=a+b+1 for all a,binZZ .

On the set Z of all integers a binary operation * is defined by a*b=a+b+2 for all a,b in Z. Write the inverse of 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