Without actually computing them, but using appropriate sketches, tell if the Fourier transforms of the signals given below are real, imaginary, or neither; even, odd, or neither. Give your reasoning in each case. 

(a) x₁(t) = II (t + 1/2) - II (t - 1/2)

(b) x₂(t) = II(t/2) + II (t) 

(c) x₃(t) = sin(2πt) II (t) 

(d) x₄(t) = sin (2πt + π/4) II (t) 

(e) x₅ (t) = cos (2πt) II (t) 

(f) x₆ (t) = 1/ [1 + (t/5)⁴]