Draw structures corresponding to the following systematic names:
(a) $(4 E)-2,4$ -Dimethyl-1,4-hexadiene
(b) $c i s-3,3$ -Dimethyl- 4 -propyl-1,5-octadiene
(c) 4 -Methyl-1,2-pentadiene
(d) $(3 E, 5 Z)-2,6$ -Dimethy $1-1,3,5,7$ -octatetraene
(e) 3 -Butyl-2-heptene
(f) trans-2,2,5,5-Tetramethyl-3-hexene