The dependant Sino-Korean noun 겸 is used to depict addtiona, combination, consurrence or dual purpose. It can occur first of all between two nouns.
거실 겸 침실 a living room-cum-lunch
편집인 겸 발행인 an editor-cum-publisher
아침겸점심을 먹었어요. I ate brunch. (breakfast/lunch)
그 분은 기사겸사진사예요. He/she is a journalist/photographer.
Note that, unrelated to its use as a dependant noun, 겸 may also appear in Sino-Korean compound words such as 겸상(a table for two), 겸직(addtional work that is outside of your regular job), and 겸하다(to hold an additional position).
This pattern is applied when listing two or more joint purposes for performing a single action. This pattern can only appear with processive verbs.
-ㄹ 겸 / -을 겸
만나다, 쇼핑하다, 읽다, 공부하다...
만날 겸 쇼핑할 겸 읽을 겸 공부할 겸 ...
There is also a pattern '-을 겸 해서' with only one example listed, which is used to focus on one out of many. In this case it means that the speaker is choosing only one of two or more intentions to do something. This expression allow the listener to infer that the speaker has other intentions even though they are not explicitly stated. *It is most often used with the particle '도'.
쇼핑도 하고 영화도 볼겸 명동에 갔어요. I went to Myeongdong to go shopping and watch a movie.
한국 친구도 사귈 겸 한국말도 배울 겸 한국에 왔어요. I came to Korea to make some Korean friends and also study Korean.
운동도 할 겸 한국의 전통문화도 배울 겸 해서 요즘 태권도를 배우고 있어요. I am learning taekwondo these days to get some exercise and also learn about traditional Korean culture.
책도 읽을 겸 공부도 할 겸 도서관에 가려고 해요. I am planning to go the library to read some books and also study.
기분 전환도 할 겸 쇼핑도 할 겸 명동에 갔어요. I went to Myeongdong both to relax and do some shopping.
바람도 쐬고 친구도 만날 겸 부산에 갔어요. I went to Busan to enjoy the breeze and meet my friends, too.
칵테일도 마시고 좋은 음악도 들을 겸 재즈 바에 갔어요. We went to a jazz bar to drink cocktails and listen to nice music.
손자도 볼 겸 딸도 만날 겸해서 왔어요. I've some to see my daughter and see my grandson at the same time.
구경도 할 겸 기분 전환도 할 겸 해서 여행을 떠나려고 해요. I am planning to go on a trip so as to combine some sightseeing with a change of pace.
<참고> 강현화 외(2016), 한국어교육 문법 자료편, 한글파크, 467-468. Jaehoon Yeon and Lucien Brown(2011), Korean: A comprehensive Grammar, 40, 392. Laura Kingdon(2015), Essential Korean Grammar, Tuttle, 49, 95-96. 민진영 외(2011), Korean Grammar in Use Intermediate, Darakwon, 124-125.