R D Sharma Solutions for Chapter: Binary Operations, Exercise 1: EXERCISE

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 the set of all rational numbers except $-1$ with respect to $*$ defined by $a*b=a+b+ab$.

If the binary operation $*$ on the set $Z$is defined by $a*b=a+b-5$, the find the identity element with respect to $*$.

On the set $Z$of integers, if the binary operation $*$ is defined by $a*b=a+b+ 2$, then find the identity element.