Consider the following two statements:

$\left(A\right)$ An emf can be induced by moving a conductor in a magnetic field.

$\left(B\right)$ An emf can be induced by changing the magnetic field.

The correct option is A Both $A$ and $B$ are true.
We know that when we move a conductor in a magnetic field, then an emf is induced across its end.

The emf induced is given by the equation,
$e=Bvl$

Hence, statement $A$ is correct.

Also, we know that if a coil lies in a magnetic field and if the magnetic field is changed, the flux linked with the coil also changes and hence an emf is induced in the coil according to the equation, $e=-\frac{d\varphi }{dt}$

Hence, statement $B$ is also correct.

Therefore, option $\left(A\right)$ is the correct answer.