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Sets \( B \) and \( D \) are subsets of the universal set \( U \). These sets are defined as follows. \[ \begin{array}{l}U=\{f, k, r, x, z\} \\ B=\{f, k, x\} \\ D=\{f, r, x\}\end{array} \] Find the following sets. Write your answer in roster form or as \( \varnothing \). (a) \( B \cap D^{\prime}=\square \)

Obtain convolution of \( \begin{aligned} x(t) & =2 \text { for }-2 \leq t \leq 2 & \& h(t) & =4 \text { for } 0 \leq t \leq 2 \\ & =0 \text { otherwise } & & =0 \text { otherwise }\end{aligned} \)

The input voltage to the \( R C \) circuit is given as \( \boldsymbol{x}(t)=t e^{-t / R C} u(t) \) and impulse response of the circuit is given by \( \mathbf{h}(\mathbf{t})=\frac{\mathbf{1}}{\mathbf{R C}} e^{-t / R C} \mathbf{u}(t) \) Find the output \( y(t) \).

Sets \( A \) and \( B \) are subsets of the universal set \( U \). These sets are defined as follows. \[ \begin{array}{l}U=\{1,3,5,7,8\} \\ A=\{3,5,8\} \\ B=\{1,3\}\end{array} \] Find the following sets. Write your answer in roster form or as \( \varnothing \). (a) \( (A \cap B)^{\prime}=\square \) (b) \( A^{\prime} \cup B=\square \)

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