Let ∗ be a binary operation on the set Q of rational number as follo

1.	Let ∗ be a binary operation on the set Q of rational number as follows: (i)a∗b=a−b (ii)a∗b=a2+b2 (iii)a∗b=a+ab (iv)a∗b=(a−b)2 (v)a∗b=ab4 (vi)a∗b=ab2 Show that none of the operation has identity.
Answer» Let $$ be a binary operation on the set Q of rational number as follows: $(i) a b = a - b$ $(i i) a * b = a^{2} + b^{2}$ $(i i i) a * b = a + a b$ $(i v) a * b = (a - b)^{2}$ $(v) a * b = \frac{a b}{4}$ $(v i) a * b = a b^{2}$ Show that none of the operation has identity.

Let ∗ be a binary operation on the set Q of rational number as follows: (i)a∗b=a−b (ii)a∗b=a2+b2 (iii)a∗b=a+ab (iv)a∗b=(a−b)2 (v)a∗b=ab4 (vi)a∗b=ab2 Show that none of the operation has identity.

Answer»

Let $*$ be a binary operation on the set Q of rational number as follows:
$(i) a * b = a - b$

$(i i) a * b = a^{2} + b^{2}$

$(i i i) a * b = a + a b$

$(i v) a * b = (a - b)^{2}$

$(v) a * b = \frac{a b}{4}$

$(v i) a * b = a b^{2}$
Show that none of the operation has identity.