Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system relations $\mathrm{R} 1, \mathrm{R} 2, \mathrm{R} 3, \mathrm{R} 4 .$
$$\begin{array}{ll} \qquad \qquad \quad \textbf{Properties} & \quad \textbf{Relations} \\ \text{P1: Linear but NOT time-invariant} & \mathrm{R} 1: y(t)=t^{2} x(t) \\ \text{P2: Time-invariant but NOT linear} & \mathrm{R} 2: y(t)=t|x(t)| \\ \text{P3: Linear and time-invariant} & \mathrm{R} 3: y(t)=|x(t)| \\ & \mathrm{R} 4: y(t)=x(t-5) \end{array}$$
- $\text{(P1, R1), (P2, R3), (P3, R4)}$
- $\text{(P1, R2), (P2, R3), (P3, R4)}$
- $\text{(P1, R3), (P2, R1), (P3, R2)}$
- $\text{(P1, R1), (P2, R2), (P3, R3)}$
