Possible Outcomes (whether X or Y): 든지

든지 is used after each option a sequence of possible options. The sequence is usually followed by a statement of what will or should happen regardless. It roughly translates to “Whether you do X or Y, it doesn’t matter/the outcome should/will be…”:

버스를 타든지 택시를 타든지 저기까지 오랫동안 걸려요.
Whether you take a bus or a taxi, it takes a long time to get there.

가든지 안 가든지 신경 안 써!
I don’t care whether you stay or go!

텔레비존을 보든지 게임을 하든지 마음대로 하세요.
Whether you watch TV or play computer games, please do as you wish.

If there are only two opposing choices, the second can be replaced with 말든지 (from 말다to be not)

남자친구 좋아하든지 말든지 결혼 할 거에요.
Whether you like my boyfriend or not we’re still getting married.

밥을 먹든지 말든지 나중에 집 밖에 가고싶어요.
Whether we eat or not, I want to go out later.

Redundant verbs in the first clause can be replaced with 이다 if the meaning remains clear:

보수당를 투표하든지 노동당를 투표하든지 선거에 투표하세요!
보수당이든지 노동당이든지 선거에 꼭 투표하세요!
Whether you vote for the Conservative Party or the Labour Party, please vote in the election!

중국음식이든지 태국음식이든지 지금은 일단 먹읍시다!
Whether it’s Chinese or Thai food, let’s eat now!