A binary operation \star is defined on the set of real numbers \mathbb{R} by a \star b = a… — JAMB UTME

A binary operation $\star$ is defined on the set of real numbers $\mathbb{R}$ by $a \star b = a + b + 7$ . What is the identity element of the operation?

$-7$ Answer
B
$7$
C
$0$
D
$-1$

Answer

The identity element of the operation is

-7

For an identity element

e

, the condition

a \star e = a

must hold for all real numbers

a

. Substituting the operation definition gives

a + e + 7 = a

. Subtracting

a

from both sides results in

e + 7 = 0

, which solves to

e = -7

Step-by-Step Solution

Set up the defining equation for the identity element

e

a \star e = a

By definition, an identity element

e

leaves any element

a

unchanged under the operation.

Apply the given rule for the binary operation.

a + e + 7 = a

The binary operation is defined as

a \star b = a + b + 7

Solve for

e

e = -7

Subtracting

a + 7

from both sides gives

e = -7

Key Concept

Identity element of a binary operation

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