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Some musings below:

The first thing that strikes us as peculiar about rule B is:

That it only applies for numbers from 1 to 3999

Aha! Perhaps the rule is about

Roman numerals?

In particular,

It looks like the number of Is in a particular number's representation is inconsequential.

So, perhaps these sets represent:

The numbers from 0 onwards in order?

To find such a bijection,

Consider I→0, V→1, X→2, L→3, C→4, D→5 and M→6 and add up the letters within a particular number's representation.

This does account for all the equivalences in the rule. However,

Some numbers are missing, such as 54 through 58 which would have a total of (ignoring any Is) LV→3+1=4 so should fit under 19's header (19=XIX→2+0+2=4).

Under this (flawed) approach, the answer to question 2 would then be:

44=XLIV→2+3+0+1=6 so it should fit under 29's equivalence class. Under this interpretation, a full (I think) list of numbers in this class would be 29 through 33 (XXX), 44 through 48 (XLV), 64 through 68 (LXV), 89 through 93 (XC), 109 through 113 (CX), 504 through 508 (DV) and 1000 through 1003 (M).

If a similar approach were to be applied to the original question,

We might be looking for a number system going from 0 to 99 with numbers represented by their distance to the nearest multiple of 20, such that multiples of 20 all have the same non-zero "value", but I can't think of an applicable system off the top of my head.

Further digging suggests:

The missing values are those with two "multiple of 5 counters", i.e. two of those of VLD. (Perhaps those with more are missing, but we would need to get up to a sum of 9 to confirm.)

Using this reasoning, perhaps:

Those values are in some separate category for some yet-to-be understood reasoning.

In which case the answer to question 2 would be:

44 would be equal to 44 through 48 (XLV), 64 to 68 (LXV) and 504 through 509 (DV).

Some musings below:

The first thing that strikes us as peculiar about rule B is:

That it only applies for numbers from 1 to 3999

Aha! Perhaps the rule is about

Roman numerals?

In particular,

It looks like the number of Is in a particular number's representation is inconsequential.

So, perhaps these sets represent:

The numbers from 0 onwards in order?

To find such a bijection,

Consider I→0, V→1, X→2, L→3, C→4, D→5 and M→6 and add up the letters within a particular number's representation.

This does account for all the equivalences in the rule. However,

Some numbers are missing, such as 54 through 58 which would have a total of (ignoring any Is) LV→3+1=4 so should fit under 19's header (19=XIX→2+0+2=4).

Under this (flawed) approach, the answer to question 2 would then be:

44=XLIV→2+3+0+1=6 so it should fit under 29's equivalence class. Under this interpretation, a full (I think) list of numbers in this class would be 29 through 33 (XXX), 44 through 48 (XLV), 64 through 68 (LXV), 89 through 93 (XC), 109 through 113 (CX), 504 through 508 (DV) and 1000 through 1003 (M).

If a similar approach were to be applied to the original question,

We might be looking for a number system going from 0 to 99 with numbers represented by their distance to the nearest multiple of 20, such that multiples of 20 all have the same non-zero "value", but I can't think of an applicable system off the top of my head.

Further digging suggests:

The missing values are those with two "multiple of 5 counters", i.e. two of those of VLD. (Perhaps those with more are missing, but we would need to get up to a sum of 9 to confirm.)

Using this reasoning, perhaps:

Those values are in some separate category for some yet-to-be understood reasoning.

In which case the answer to question 2 would be:

44 would be equal to 44 through 48 (XLV), 64 to 68 (LXV) and 504 through 508 (DV).

Some musings below:

The first thing that strikes us as peculiar about rule B is:

That it only applies for numbers from 1 to 3999

Aha! Perhaps the rule is about

Roman numerals?

In particular,

It looks like the number of Is in a particular number's representation is inconsequential.

So, perhaps these sets represent:

The numbers from 0 onwards in order?

To find such a bijection,

Consider I→0, V→1, X→2, L→3, C→4, D→5 and M→6 and add up the letters within a particular number's representation.

This does account for all the equivalences in the rule. However,

Some numbers are missing, such as 54 through 58 which would have a total of (ignoring any Is) LV→3+1=4 so should fit under 19's header (19=XIX→2+0+2=4).

Under this (flawed) approach, the answer to question 2 would then be:

44=XLIV→2+3+0+1=6 so it should fit under 29's equivalence class. Under this interpretation, a full (I think) list of numbers in this class would be 29 through 33 (XXX), 44 through 48 (XLV), 64 through 68 (LXV), 89 through 93 (XC), 109 through 113 (CX), 504 through 508 (DV) and 1000 through 1003 (M).

If a similar approach were to be applied to the original question,

We might be looking for a number system going from 0 to 99 with numbers represented by their distance to the nearest multiple of 20, such that multiples of 20 all have the same non-zero "value", but I can't think of an applicable system off the top of my head.

Some musings below:

The first thing that strikes us as peculiar about rule B is:

That it only applies for numbers from 1 to 3999

Aha! Perhaps the rule is about

Roman numerals?

In particular,

It looks like the number of Is in a particular number's representation is inconsequential.

So, perhaps these sets represent:

The numbers from 0 onwards in order?

To find such a bijection,

Consider I→0, V→1, X→2, L→3, C→4, D→5 and M→6 and add up the letters within a particular number's representation.

This does account for all the equivalences in the rule. However,

Some numbers are missing, such as 54 through 58 which would have a total of (ignoring any Is) LV→3+1=4 so should fit under 19's header (19=XIX→2+0+2=4).

Under this (flawed) approach, the answer to question 2 would then be:

44=XLIV→2+3+0+1=6 so it should fit under 29's equivalence class. Under this interpretation, a full (I think) list of numbers in this class would be 29 through 33 (XXX), 44 through 48 (XLV), 64 through 68 (LXV), 89 through 93 (XC), 109 through 113 (CX), 504 through 508 (DV) and 1000 through 1003 (M).

If a similar approach were to be applied to the original question,

We might be looking for a number system going from 0 to 99 with numbers represented by their distance to the nearest multiple of 20, such that multiples of 20 all have the same non-zero "value", but I can't think of an applicable system off the top of my head.

Further digging suggests:

The missing values are those with two "multiple of 5 counters", i.e. two of those of VLD. (Perhaps those with more are missing, but we would need to get up to a sum of 9 to confirm.)

Using this reasoning, perhaps:

Those values are in some separate category for some yet-to-be understood reasoning.

In which case the answer to question 2 would be:

44 would be equal to 44 through 48 (XLV), 64 to 68 (LXV) and 504 through 509 (DV).

Some musings below:

The first thing that strikes us as peculiar about rule B is:

That it only applies for numbers from 1 to 3999

Aha! Perhaps the rule is about

Roman numerals?

In particular,

It looks like the number of Is in a particular number's representation is inconsequential.

So, perhaps these sets represent:

The numbers from 0 onwards in order?

To find such a bijection

Consider I→0, V→1, X→2, L→3, C→4, D→5 and M→6 and add up the letters within a particular number's representation.

This does account for all the equivalences in the rule. However

Some numbers are missing, such as 54 through 58 which would have a total of (ignoring any Is) LV→3+1=4 so should fit under 19's header (19=XIX→2+0+2=4).

But if this is correct, the answer to question 2 would be

44=XLIV→2+3+0+1=6 so it should fit under 29's equivalence class. Under this interpretation, a full (I think) list of numbers in this class would be 29 through 33 (XXX), 44 through 48 (XLV), 64 through 68 (LXV), 89 through 93 (XC), 109 through 113 (CX), 504 through 508 (DV) and 1000 through 1003 (M).

Some musings below:

The first thing that strikes us as peculiar about rule B is:

That it only applies for numbers from 1 to 3999

Aha! Perhaps the rule is about

Roman numerals?

In particular,

It looks like the number of Is in a particular number's representation is inconsequential.

So, perhaps these sets represent:

The numbers from 0 onwards in order?

To find such a bijection,

Consider I→0, V→1, X→2, L→3, C→4, D→5 and M→6 and add up the letters within a particular number's representation.

This does account for all the equivalences in the rule. However,

Some numbers are missing, such as 54 through 58 which would have a total of (ignoring any Is) LV→3+1=4 so should fit under 19's header (19=XIX→2+0+2=4).

Under this (flawed) approach, the answer to question 2 would then be:

44=XLIV→2+3+0+1=6 so it should fit under 29's equivalence class. Under this interpretation, a full (I think) list of numbers in this class would be 29 through 33 (XXX), 44 through 48 (XLV), 64 through 68 (LXV), 89 through 93 (XC), 109 through 113 (CX), 504 through 508 (DV) and 1000 through 1003 (M).

If a similar approach were to be applied to the original question,

We might be looking for a number system going from 0 to 99 with numbers represented by their distance to the nearest multiple of 20, such that multiples of 20 all have the same non-zero "value", but I can't think of an applicable system off the top of my head.