I have the following slogan:
I sell, I build
I want to make sure it's clear and concise. I did not add a period, because I know it's not a full sentence. However, I want to make sure it's grammatically correct.
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Think of slogans as upside-down kanji tattooed on a non-Japanese-speaking person's shoulder blade: decorative, rather than an attempt to convey meaningful information. Whether a slogan should obey the rules of grammar or make sense are secondary concerns to how it looks on a billboard. Not convinced? Here are some examples found in the wild:
Notice how 'I' is not capitalized. It's a deliberate choice made by the company to drive home they are a fast food chain and you don't have to dress up to eat there.
As written this is a command to ponder the abstract concept of 'different' rather than a command to change your mindset and consider purchasing one of their products. (The latter would read 'think differently,' but that adds two characters and long words aren't sleek.)
I love this slogan. It's so bad. Need I point out 'car' isn't a verb? Why they chose it, no idea. Maybe the slogan rhymes if you pronounce 'are' as 'ar?'
In conclusion, don't worry over grammatical correctness. Worry over whether inclusion of a period makes your company look stuffy or if changing the font color from lime green to hot pink makes it harder to see when printed on a promotional T-shirt.
I sell, I build
You say it's not a sentence. It is actually two complete sentences, "I sell." and "I build."
If you search online for a very famous 'slogan': Veni, Vidi, Vici, you will see many punctuations for this. Some have commas, some have full-stops, some are in upper case, some are in lower case.
If you look at these examples, you may see one that best suits you. Note that it may depend on whether the sentences are next to each other or above each other.