It is from my intermediate Korean textbook. Here it teaches the pattern "지(요), 뭘". But what does this pattern mean?

My textbook has an explanation but the explanation is quite short, so I cannot quite grasp the meaning.
It is ideal if you can also tell me the Japanese translation of this pattern, too. (I failed to find any web source which explain this pattern, either in Japanese or English.)

Below are the examples sentence of the pattern:

가: 교수님께서도 술 한 잔 하시지요, 뭘.
나: 저는 술은 못하니까 와인이나 한잔 합시다.

가: 다음 주에 우리는 동남아 여행을 가는데 왕명 씨도 함께 가시지요, 뭘.
나: 저는 다음 주에 학위 논문 심의가 있어서 발표 준비를 해야 합니다.

가: 폭우가 쏟아질 것 같아요. 준비를 안 해도 괜찮겠어요?
나: 폭우가 쏟아질테면 쏟아지라지요, 뭘. 이미 준비를 다 한걸요.

가: 백주이 없으면 백주라도 마시지요, 뭘.
나: 저는 맥주를 마시면 속탈이 생겨서 안 마시겠습니다.

 

1. Alas! It probably is the most difficult to explain the meaning of any interjection. My oh my.

2. If you really have to know, please note that 뭘 is a shortened form of 무얼, which is also a shortened form of 무엇을.
In those examples, it might suggest "무엇을 망설이십니까? (What are you waiting for?)" or "What do you hesitate for?", even "Whatever" (for your third example)

3. But I don't think it is that bright idea to relate the meaning of "뭘" here to 무엇(what).
English speakers call the name of Jesus all the time, even when they are atheists. They exclaim "son of a bitch" even at a woman.
Interjection is all about subtle nuances, with no concrete meanings.

 

How do you translate the example sentences with 지요, 뭘?
This helps me better to arrive at a better understanding.

Actually, my book (a Chinese book) says it means "there is nothing that the listener cannot do" (聽話的人一起做後面的動作也沒有什麼不可以).