The input x(t) and the corresponding output y(t) of a linear time-invariant (LTI) system are

x(t) = u(t) − u(t − 1) → y(t) = r(t) − 2r(t − 1) + r(t − 2)

Determine the outputs y_i(t), i = 1, 2, 3 corresponding to the following inputs

(a) x₁(t) = u(t) − u(t − 1) − u(t − 2) + u(t − 3),

(b) x₂(t) = u(t + 1) − 2u(t) + u(t − 1),

(c) x₃(t) = δ(t) − δ(t − 1)

Plot the inputs x_i(t) and the corresponding output y_i(t).