The pairs among A = [SO_3^ 2- , CO_3^ 2- ] , B = [O_2^ 2- , F_2] ,...

Species with the same number of valence electrons and the same skeletal structure generally have similar Lewis dot structures (isoelectronic species).

For pair A: $\text{SO}_3^{2-}$ has $6 + 3(6) + 2 = 26$ valence electrons. $\text{CO}_3^{2-}$ has $4 + 3(6) + 2 = 24$ valence electrons. Since they have different numbers of valence electrons, they do not have similar Lewis dot structures ($\text{SO}_3^{2-}$ has a lone pair on the central atom and is pyramidal, while $\text{CO}_3^{2-}$ has no lone pair on the central atom and is trigonal planar).

For pair B: $\text{O}_2^{2-}$ has $2(6) + 2 = 14$ valence electrons. $\text{F}_2$ has $2(7) = 14$ valence electrons. Both have a single bond and three lone pairs on each atom, so they have similar Lewis dot structures.

For pair C: $\text{CN}^-$ has $4 + 5 + 1 = 10$ valence electrons. $\text{CO}$ has $4 + 6 = 10$ valence electrons. Both have a triple bond and one lone pair on each atom, so they have similar Lewis dot structures.

For pair D: $\text{NH}_3$ has $5 + 3(1) = 8$ valence electrons. $\text{H}_3\text{O}^+$ has $6 + 3(1) - 1 = 8$ valence electrons. Both have three single bonds and one lone pair on the central atom, so they have similar Lewis dot structures.

For pair E: $\text{MnO}_4^{2-}$ has $7 + 4(6) + 2 = 33$ valence electrons. $\text{CrO}_4^{2-}$ has $6 + 4(6) + 2 = 32$ valence electrons. Since they have different numbers of valence electrons ($\text{MnO}_4^{2-}$ has an unpaired electron), they do not have similar Lewis dot structures.

Thus, pairs A and E do not have similar Lewis dot structures.

Answer: A and E