Step 1: Recall what natural rubber is.
Natural rubber is the addition polymer cis-1,4-polyisoprene, so its monomer is isoprene, a conjugated diene with a methyl branch.
Step 2: Write the monomer X.
Isoprene is 2-methyl-1,3-butadiene: $CH_2=C(CH_3)-CH=CH_2$. So $X=CH_2=C(CH_3)-CH=CH_2$.
Step 3: Recall what neoprene is.
Neoprene is polychloroprene, the addition polymer of chloroprene, a diene carrying a chlorine instead of the methyl.
Step 4: Write the monomer Y.
Chloroprene is 2-chloro-1,3-butadiene: $CH_2=C(Cl)-CH=CH_2$. So $Y=CH_2=C(Cl)-CH=CH_2$.
Step 5: Eliminate wrong options.
Choices using a $CN$, $C_2H_5$, or $C_6H_5$ group in place of the methyl or chlorine do not represent isoprene and chloroprene, so they are rejected.
Step 6: Choose the correct pair.
$X=CH_2=C(CH_3)-CH=CH_2$ and $Y=CH_2=C(Cl)-CH=CH_2$ matches option (1).
\[ \boxed{X=CH_2{=}C(CH_3){-}CH{=}CH_2,\ \ Y=CH_2{=}C(Cl){-}CH{=}CH_2\ \ \text{(Option 1)}} \]