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...with examples from Stargate Atlantis and NCIS...
Question: Which is correct, "X's and Y's" or "X and Y's"?
First, let me try to make it clear that this question involves plurals and not possessives. Both forms use an apostrophe ( ' ) plus the letter s, but plurals apply to each noun in a series while possessives apply to only the last noun.
Plurals "It's raining cats and dogs out here, Boss!" Tony shouted over the weather into his phone.
Possessives Startled by John and Rodney's model cars, Teyla scolded the men for acting like children.
So, just as you would when referring to more than one person, place, or thing, you should use the plural form of each letter that is not singular. So, if you are indeed talking about more than one X in addition to more than one Y, both letters should be followed by -s or -'s.
From an early age, John's father promised him a new model plane for each math test he passed. John made sure to achieve A's and B's from then on.
If you use combined letters as an abbreviation for a single compound noun, you would treat that combination as one letter.
The new NCIS recruits had lined up Q&A's with various senior team members.
Regarding when and when not to use an apostrophe, it depends on if you are using capital or lowercase letters as well as what style manual you follow. Please see the Grammar 101 post (once it's written!) for more on apostrophes. As always, once you have decided on usage, stay consistent with that usage throughout your whole piece.
Resources:
Hodges' Harbrace Handbook, Fifteenth Edition (Cheryl Glenn, Robert Keith Miller, and Suzanne Strobeck Webb)
Question: Which is correct, "X's and Y's" or "X and Y's"?
First, let me try to make it clear that this question involves plurals and not possessives. Both forms use an apostrophe ( ' ) plus the letter s, but plurals apply to each noun in a series while possessives apply to only the last noun.


So, just as you would when referring to more than one person, place, or thing, you should use the plural form of each letter that is not singular. So, if you are indeed talking about more than one X in addition to more than one Y, both letters should be followed by -s or -'s.

If you use combined letters as an abbreviation for a single compound noun, you would treat that combination as one letter.

Regarding when and when not to use an apostrophe, it depends on if you are using capital or lowercase letters as well as what style manual you follow. Please see the Grammar 101 post (once it's written!) for more on apostrophes. As always, once you have decided on usage, stay consistent with that usage throughout your whole piece.
Resources:
Hodges' Harbrace Handbook, Fifteenth Edition (Cheryl Glenn, Robert Keith Miller, and Suzanne Strobeck Webb)