Question

Let f : Z→ $Z_2$, be a homomorphism of groups defined by
$f(a) = \begin{cases} 0, & \quad \text{if } a \text{ is even}\\\ 1, & \quad \text{if } a \text{ is odd} \end{cases}$

then Kerf is :

• A. The set of all odd integers
• B. The set of all even integers
• C. The set of all natural numbers
• D. The set of all real numbers

Answer 1

Answer: (B)

The set of all even integers

Answer 2

The correct option is(B):The set of all even integers