# "And " vs "Or" when using respectively

I want to reduce my sentence to a shorter sentence. My actual intention is:

In real-type representations, k is 1, in complex-type representations, k is 2, and in quaternion-type representations, k is 4.

I wrote it as follows:

k is 1, 2, and 4 for real-type, complex-type, and quaternion-type irreducible representation, respectively.

However, my supervisor said the correct sentence is:

k is 1, 2, or 4 for real-type, complex-type, or quaternion-type irreducible representation, respectively.

I thought, since in the actual sentence I have "and", in the reduced one I need to use "and". However, because it is describing three distinct cases and each case is exclusive, we need to use "or".

Would someone explain this to me? In grammatical English classes, I have learned to think like the first case.

• I'd be tempted to leave out the first coordinator. k is 1, 2, 4 for real-type, complex-type, and quaternion-type irreducible representations, respectively. Commented Jun 17 at 18:03
• I think you can use either, as long as you're consistent. But I also think "or" is more common. Commented Jun 17 at 18:05
• If k=1 for real-types, there's no choice. I'd interpret or to say there's a choice. Anyway, more compact isn't always clearer. Commented Jun 17 at 20:21
• Me? I'd prefer to read, "for r-type, c-type, and q-type reps, k is 1, 2, and 4 respectively." (contractions used for brevity.) State the set of (familiar?) invariant categories first, then the set of corresponding value for each of those categories. Because each of the two 'sets' has several elements, "and" within each 'set' would be more natural. "For X, Y and Z, use 7, 11 and 13"
– user506571
Commented Jun 17 at 22:42
• Whatever the technically correct answer to the question, as posed, is, the best thing to do is use the very first, long, version, and not attempt to shorten it. Shortening the sentence saves a very small amount of space at the price of imposing extra work on the reader and creating a risk of a misunderstanding. Commented Jun 19 at 17:09

k is 1, 2, and 4 for real-type, complex-type, and quaternion-type irreducible representation, respectively.

k is 1, 2, or 4 for real, complex, and quaternion type representations respectively.

However I suspect that the concept of a "type representation" is not needed as these could just be "types".

Within mathematics Real, Complex, and Quaternion are respectively 1, 2 and 4 dimensional rings, a ring is type of abstract algebraic structure with many useful mathematical properties.

• Lower-casing of designated variables/constants trumps other demands such as being sentence-initial. g, for instance, must not be confused with G. Commented Jun 18 at 15:35

This statement mostly clearly and concisely reflects your intended meaning:

• For real-, complex- and quaternion-type representations, the value of k is 1, 2 and 4, respectively.

my supervisor said that the correct sentence is:

k is 1, 2, or 4 for real-type, complex-type, or quaternion-type irreducible representation, respectively.

because it is describing three distinct cases and each case is exclusive, we need to use "or".

There is no particular basis for assuming that the disjunction in "...or.....or..., respectively" should be exclusive; after all, the conjunction in "...and.....and..., respectively" certainly does not mean that the cases overlap!

Thus, whenever "...and.....and..., respectively" is appropriate, opting for the unorthodox "...or.....or..., respectively" adds no value and just feels distractingly out of left field.

On the other hand, the following are two related "....respectively" examples (the second one from here), where opting for or instead of and is appropriate (note that neither case contravenes my previous paragraph).

• The light might turn red or amber, in which case you should press their respective buttons.
• If the light changes from red to blue or from blue to red, you must catch and throw the ball, respectively.