Let - be a binary operation on the set Q of rational number as follows-i a - b - ab -4Show that none of the operations has an identity-

An element e ∈ Q will be the identity element for the operation ∗ if a ∗ b =ab/4 If a ∗ e =a, then ae/4=a. Hence, e =4 is the identity element. ∴ a ∗ 4 =4 ∗ a = ...

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Standard XII

Mathematics

Definition of Relations

Let * be a bi...

Question

Let $$ be a binary operation on the set Q of rational number as follows:
$(i) a b = \frac{a b}{4}$
Show that none of the operations has an identity.

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Solution

An element $e \in Q$ will be the identity element for the operation $$ if
$a b = \frac{a b}{4}$
If $a * e = a, t h e n \frac{a e}{4} = a$ . Hence, e =4 is the identity element.
$∴ a * 4 = 4 * a = \frac{4 a}{4} = a$

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Let ∗ be a binary operation on the set Q of rational number as follows: (i)a∗b=ab4 Show that none of the operations has an identity.

An element e∈Q will be the identity element for the operation ∗ if a∗b=ab4 If a∗e=a,then ae4=a. Hence, e =4 is the identity element. ∴a∗4=4∗a=4a4=a

Let $$ be a binary operation on the set Q of rational number as follows:
$(i) a b = \frac{a b}{4}$
Show that none of the operations has an identity.

An element $e \in Q$ will be the identity element for the operation $$ if
$a b = \frac{a b}{4}$
If $a * e = a, t h e n \frac{a e}{4} = a$ . Hence, e =4 is the identity element.
$∴ a * 4 = 4 * a = \frac{4 a}{4} = a$