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

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

Answer: -7

Answer

The identity element under the operation is

-7

The identity element

e

satisfies

a \ast e = a

for any real number

a

. Substituting into the definition gives

a + e + 7 = a

, which simplifies to

e = -7

Step-by-Step Solution

Set up the identity element equation using the definition

a \ast e = a

a + e + 7 = a

By definition, operating any element

a

with the identity element

e

yields

a

Subtract

a

from both sides of the equation.

e + 7 = 0

Isolating terms involving

e

Subtract

7

from both sides to solve for

e

e = -7

Determining the numerical value of the identity element.

Key Concept

Identity Element in Binary Operations

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