You are right that also for the second signal you have $M(\omega)\neq A(\omega)$, but the point here probably is that in the fundamental interval $\omega\in (-\pi,\pi)$ the two are identical. It is only at $\omega=\pm\pi$ that the phase $\phi_M(\omega)$ jumps and that $A(\omega)$ changes its sign. So what they probably mean is

$$M(\omega)=A(\omega)\quad\text{and}\quad\phi_M(\omega)=\phi_A(\omega)\quad\boxed{\text{for }\omega\in(-\pi,\pi)}$$

which is correct (and which is not the case for the first signal).

Remember that such quizzes are made by fallible humans.

You are right that also for the second signal you have $M(\omega)\neq A(\omega)$, but the point here probably is that in the fundamental interval $\omega\in (-\pi,\pi)$ the two are identical. It is only at $\omega=\pm\pi$ that the phase $\phi_M(\omega)$ jumps and that $A(\omega)$ changes its sign. So what they probably mean is

$$M(\omega)=A(\omega)\quad\text{and}\quad\phi_M(\omega)=\phi_A(\omega)\quad\bbox[5px,border:2px solid red]{\text{for }\omega\in(-\pi,\pi)}$$

which is correct (and which is not the case for the first signal).

Remember that such quizzes are made by fallible humans.

You are right that also for the second signal you have $M(\omega)\neq A(\omega)$, but the point here probably is that in the fundamental interval $\omega\in [-\pi,\pi]$ the two are identical. It is only at $\omega=\pm\pi$ that the phase $\phi_M(\omega)$ jumps and that $A(\omega)$ changes its sign. So what they probably mean is

$$M(\omega)=A(\omega)\quad\text{and}\quad\phi_M(\omega)=\phi_A(\omega)\quad\boxed{\text{for }\omega\in[-\pi,\pi]}$$

which is correct (and which is not the case for the first signal).

Remember that such quizzes are made by fallible humans.

You are right that also for the second signal you have $M(\omega)\neq A(\omega)$, but the point here probably is that in the fundamental interval $\omega\in (-\pi,\pi)$ the two are identical. It is only at $\omega=\pm\pi$ that the phase $\phi_M(\omega)$ jumps and that $A(\omega)$ changes its sign. So what they probably mean is

$$M(\omega)=A(\omega)\quad\text{and}\quad\phi_M(\omega)=\phi_A(\omega)\quad\boxed{\text{for }\omega\in(-\pi,\pi)}$$

which is correct (and which is not the case for the first signal).

Remember that such quizzes are made by fallible humans.