While looking at some 수능 maths questions, I noticed some common pattern using the words 단 and 대하여. Here is an example:

전체집합 U={1,2,3,4,5,6}에 대하여 두 부분집합 A, B는 다음 조건을 만족시킨다. 두 지합 A화 B를 정하는 경우의 수는? (, n(X)는 집합 X의 원수의 개수이다.)

(가) $A\cap B=\emptyset$

(나) n(A)=1, n(B)>=1

Taking a lot of liberty with the structure of the sentence, this can be translated as

A and B are two subsets of the set U={1,2,3,4,5,6} that satisfy the 2 conditions below. In how many ways can the sets A and B be chosen? (Given, n(X) is the number of elements of the set X)

Condition 1. $A\cap B=\emptyset$

Condition 2. $n(A)=1, n(B)>=1$

My (related) questions:

  1. What are the words 단 and 대하여?
  2. How are they usually translated in English?
  3. How are they used in a non-mathematical context?

대하여 is a very common word, meaning "concerning/on/with respect to". It is actually derived from verb 대하다 (although it's probably best regarded as a separate word), and can take forms as 대하여/대해/대한.

일본에 대하여 알아보자. = Let's know more about Japan.

영문법에 대한 책 = A book on English grammar

전체집합 U에 대하여... = With respect to the universal set U...

is a connecting word used to quantify the previous sentence or explain an exception, similar to "Except that" or "Note that".

수수료는 500원입니다. , 주말에는 추가 요금이 부과될 수 있습니다. = The commission is 500 won, except that weekend surcharge may apply.

X의 값을 구하라. , X는 양수이다. = Find the value of X. Assume that X is positive.

  • 2
    The answer for 단 is very great! When I first saw the question I could not think about suitable English translation for 단. Now I think "note that" is really an excellent translation for 단. – JSong Jan 16 '18 at 10:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.