When used as a 副詞（ふくし）, 一応（いちおう） can often carry the nuance of (A) not being perfect, but the minimum required in order to prevent (B). This particular nuance of 一応（いちおう） may be interpreted as ‘just in case, (A)’, or ‘just to be sure (A)’.

• 今日（きょう）はずっと晴（は）れって天気（てんき）予報（よほう）で言（い）ってたけど曇（くも）ってきたから 一応（いちおう）傘（かさ）を持（も）って行（い）ったほうがいいかも。
  They said it was going to be sunny all day today on the forecast, but it is starting to get cloudy so it might be better to bring an umbrella just in case.
• これで大丈夫（だいじょうぶ）だと思（おも）うけど、 一応（いちおう）チェックしておいてくれない？
  I think this is fine, but just to be sure, can you please double check it for me?

When 一応（いちおう） is used this way, it frequently highlights that (B) happening is unlikely, but the precautionary measure of (A) might be a good idea to avoid it. This is in contrast to another common use of 一応（いちおう） which can be translated as ‘more or less’, or ‘for the time being’. However, in both of its uses, it simply indicates the minimum amount of (A) which is fulfilling some requirement.

• 田中（たなか）：「仕事（しごと）慣（な）れてきた？」鈴木（すずき）：「はい、 一応（いちおう）...」
  Tanaka: ‘Have you gotten used to work?’ Suzuki: ‘Yes, more or less…’
• 一応（いちおう）はよくなってるみたいですけど、また来週（らいしゅう）病院（びょういん）まで来（き）てください。
  For the time being, it seems like you are getting better, but please come to the hospital again next week.