Exercise 3.3

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

Answer: Consider, e be the identity element in I+Β with respect to * such that a * e = a = e * a, β a β Q β {-1} a * e = a and e * a = a, β a β Q β {-1} a + e + ae = a and e + a + ea = a, β a β Q β...

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

Answer: Consider, e be the identity element in I+ with respect to * a * e = a = e * a, β a β I+ a * e = a and e * a = a, β a β I+ a + e = a and e + a = a, β a β I+ e = 0, β a β I+ Hence, 0 is the...

Assume βeβ be the identity element in ${{I}^{+}}$ with respect to * such that $a*e=a=e*a,\forall a\in Q-\left\{ -1 \right\}$ $a*e=a$and $e*a=a,\forall a\in Q-\left\{ -1 \right\}$ $a+e+ae=a$and...
Assume βeβ be the identity element in ${{I}^{+}}$ with respect to * such that $a*e=a=e*a,\forall a\in {{I}^{+}}$ $a*e=a$and $e*a,\forall a\in {{I}^{+}}$ $a+e=a$ and $e+a=a$, $\forall a\in {{I}^{+}}$...