How can I prove that a set of ciphers are the encryption of a set of plaintexts? I have a set of plaintexts e.g., ["how", "are", "you"] and a sender who encrypts each element with a unique symmetrical key (or not) and outputs the set of ciphers. 

Receiver needs assurance that all the ciphers he just received have a one-to-one mapping with the ["how", "are", "you"] and not some other values. I'm not using asymmetric encryption because it'd reveal which cipher represents which item.

I have read all other questions and a few papers on set membership, pederson commits, etc but still can't understand how it'd work. It'd be very helpful if you could give a detailed answer.
If you are allowing for probabilistic proofs, simply have the one doing the encryption encrypt the set multiple times. All of these encrypted sets are sent to you.

You then ask the one doing the encryption to reveal the keys for all but one of the sets. You do the decryption to verify that all of those sets decrypt to the proper plaintexts. This is a cut-and-choose protocol (see Cut-and-Choose Protocol by Crépeau). 

If the adversary is going to cheat, they will only be able to encrypt one set incorrectly and you have to randomly not choose that set for verification. You can set the probability of this to be arbitrarily low (at the cost of communication and computation) by setting the number of copies of the set the one doing the encryption must encrypt to be high enough.